F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2024
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science - Timetable
- Mon 19. 2. to Sun 26. 5. Wed 12:00–14:50 F2 6/2012
- Timetable of Seminar Groups:
F2182/02: Mon 19. 2. to Sun 26. 5. Fri 12:00–12:50 F3,03015, P. Musilová - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Physics (programme PřF, B-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics. Linear and multilinear algebra is one of the most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important features and properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
- Learning outcomes
- Absolving the discipline student obtains following knowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Self-adjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- required literature
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
- recommended literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2025
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Physics (programme PřF, B-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics. Linear and multilinear algebra is one of the most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important features and properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
- Learning outcomes
- Absolving the discipline student obtains following knowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Self-adjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- required literature
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
- recommended literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
The course is taught: every week.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2023
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)
Mgr. Martina Havlíčková (assistant) - Guaranteed by
- prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science - Timetable
- Wed 8:00–10:50 F1 6/1014
- Timetable of Seminar Groups:
F2182/02: Mon 11:00–11:50 F3,03015, P. Musilová - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Physics (programme PřF, B-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics. Linear and multilinear algebra is one of the most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important features and properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
- Learning outcomes
- Absolving the discipline student obtains following knowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Self-adjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- required literature
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
- recommended literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2022
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)
Mgr. Martina Havlíčková (assistant) - Guaranteed by
- prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science - Timetable
- Wed 12:00–14:50 F1 6/1014
- Timetable of Seminar Groups:
F2182/02: Tue 11:00–11:50 F3,03015, P. Musilová - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Physics (programme PřF, B-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics. Linear and multilinear algebra is one of the most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important features and properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
- Learning outcomes
- Absolving the discipline student obtains following knowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Self-adjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- required literature
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
- recommended literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2021
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)
Bc. Peter Burda (assistant)
BcA. Hana Eliášová (assistant)
Mgr. Martina Havlíčková (assistant) - Guaranteed by
- prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science - Timetable
- Mon 1. 3. to Fri 14. 5. Wed 9:00–11:50 F1 6/1014
- Timetable of Seminar Groups:
F2182/02: Mon 1. 3. to Fri 14. 5. Tue 15:00–15:50 F1 6/1014 - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Physics (programme PřF, B-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics. Linear and multilinear algebra is one of the most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important features and properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
- Learning outcomes
- Absolving the discipline student obtains following knowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Self-adjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- required literature
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
- recommended literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2020
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science - Timetable
- Wed 12:00–14:50 F2 6/2012
- Timetable of Seminar Groups:
F2182/01: Wed 15:00–15:50 F4,03017, P. Musilová - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Physics (programme PřF, B-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics. Linear and multilinear algebra is one of the most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important features and properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
- Learning outcomes
- Absolving the discipline student obtains following knowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Self-adjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- required literature
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
- recommended literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2019
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)
RNDr. Jan Janík, Ph.D. (assistant)
Mgr. Marianna Kustyánová (assistant) - Guaranteed by
- prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science - Timetable
- Mon 18. 2. to Fri 17. 5. Wed 8:00–10:50 F4,03017
- Timetable of Seminar Groups:
- Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Physics (programme PřF, B-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics.
Linear and multilinear algebra is one of the most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important features and properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
Absolving the discipline student obtains following knowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Self-adjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- required literature
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
- recommended literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of Sciencespring 2018
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)
RNDr. Jan Janík, Ph.D. (assistant)
Mgr. Marianna Kustyánová (assistant) - Guaranteed by
- prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science - Timetable
- Mon 8:00–10:50 F1 6/1014
- Timetable of Seminar Groups:
- Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Physics (programme PřF, B-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics.
Linear and multilinear algebra is one of the most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important features and properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
Absolving the discipline student obtains following knowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Self-adjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- required literature
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
- recommended literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2017
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science - Timetable
- Mon 20. 2. to Mon 22. 5. Wed 10:00–12:50 F2 6/2012
- Timetable of Seminar Groups:
F2182/02: Mon 20. 2. to Mon 22. 5. Tue 11:00–11:50 F4,03017, P. Musilová - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Physics (programme PřF, B-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics.
Linear and multilinear algebra is one of the most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important features and properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
Absolving the discipline student obtains following knowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Self-adjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- required literature
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
- recommended literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2016
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science - Timetable
- Tue 12:00–14:50 F1 6/1014
- Timetable of Seminar Groups:
- Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Physics (programme PřF, B-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics.
Linear and multilinear algebra is one of the most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important features and properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
Absolving the discipline student obtains following knowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Self-adjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- required literature
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
- recommended literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2015
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science - Timetable
- Wed 11:00–13:50 F2 6/2012
- Timetable of Seminar Groups:
- Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Physics (programme PřF, B-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics.
Linear and multilinear algebra is one of the most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important features and properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
Absolving the discipline student obtains following knowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Self-adjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- required literature
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
- recommended literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2014
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science - Timetable
- Wed 10:00–12:50 F1 6/1014
- Timetable of Seminar Groups:
- Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Physics (programme PřF, B-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics.
Linear and multilinear algebra is one of the most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important features and properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
Absolving the discipline student obtains following knowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Self-adjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- required literature
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
- recommended literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2013
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science - Timetable
- Mon 14:00–16:50 F2 6/2012
- Timetable of Seminar Groups:
- Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Physics (programme PřF, B-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics.
Linear and multilinear algebra is one of most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important featuresand properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
Absolving the discipline student obtains following kowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Selfadjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- required literature
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
- recommended literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2012
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Michael Krbek, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science - Timetable
- Wed 8:00–10:50 F3,03015
- Timetable of Seminar Groups:
F2182/02: Thu 12:00–12:50 F4,03017 - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics.
Linear and multilinear algebra is one of most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important featuresand properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
Absolving the discipline student obtains following kowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Selfadjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- required literature
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
- recommended literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- not specified
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2011
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Michael Krbek, Ph.D. - Timetable
- Mon 9:00–11:50 F3,03015
- Timetable of Seminar Groups:
F2182/02: Fri 12:00–12:50 F3,03015, P. Musilová - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Biophysics (programme PřF, M-FY)
- Physics (programme PřF, B-FY)
- Physics (programme PřF, M-FY)
- Physics (programme PřF, N-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics.
Linear and multilinear algebra is one of most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important featuresand properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
Absolving the discipline student obtains following kowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Selfadjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2010
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Michael Krbek, Ph.D. - Timetable
- Wed 13:00–15:50 F1 6/1014
- Timetable of Seminar Groups:
F2182/02: Wed 16:00–16:50 F3,03015 - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Biophysics (programme PřF, M-FY)
- Physics (programme PřF, B-FY)
- Physics (programme PřF, M-FY)
- Physics (programme PřF, N-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics.
Linear and multilinear algebra is one of most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important featuresand properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
Absolving the discipline student obtains following kowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Selfadjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2009
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Michael Krbek, Ph.D. - Timetable
- Thu 11:00–13:50 F4,03017
- Timetable of Seminar Groups:
F2182/02: Tue 13:00–13:50 Fs1 6/1017 - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Biophysics (programme PřF, M-FY)
- Physics (programme PřF, B-FY)
- Physics (programme PřF, M-FY)
- Physics (programme PřF, N-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics.
Linear and multilinear algebra is one of most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important featuresand properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
Absolving the discipline student obtains following kowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Selfadjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2008
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Michael Krbek, Ph.D. - Timetable
- Thu 10:00–12:50 F2 6/2012
- Timetable of Seminar Groups:
F2182/02: Mon 14:00–14:50 Fs1 6/1017, P. Musilová
F2182/03: Mon 15:00–15:50 F4,03017, P. Musilová - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Biophysics (programme PřF, M-FY)
- Physics (programme PřF, B-FY)
- Physics (programme PřF, M-FY)
- Physics (programme PřF, N-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics. Linear and multilinear algebra is one of most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important featuresand properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
- Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces. 2. Scalar product, orthogonalization, orthogonal projection. 3. Linear operators in vector spaces and their representation in bases. 4. Eigenvalues and eigenvectors, diagonal representation. 5. Unitary linear operators. Selfadjoint linear operators. 6. Spectral representation. 7. Jordan normal form: Polynomial matrices and Jordan normal form. 8. Jordan normal form: JNF and invariant subspaces. 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces. 10. Tensors as linear operators, representation in bases, operations. 11. Algebraic structure of tensor spaces. 12. Exterior algebra. 13. Induced mappings of tensor spaces. 14. Physical applications-cartesian tensors.
- Literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Assessment methods (in Czech)
- Výuka: klasická prednáska, klasické cvičení. Zkouška: písemná (dvě části-(a) příklady, (b) test) a ústní.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2007
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Michael Krbek, Ph.D. - Timetable
- Wed 8:00–10:50 F2 6/2012
- Timetable of Seminar Groups:
F2182/02: Thu 15:00–15:50 F4,03017 - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Biophysics (programme PřF, M-FY)
- Physics (programme PřF, B-FY)
- Physics (programme PřF, M-FY)
- Physics (programme PřF, N-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics. Linear and multilinear algebra is one of most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important featuresand properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
- Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces. 2. Scalar product, orthogonalization, orthogonal projection. 3. Linear operators in vector spaces and their representation in bases. 4. Eigenvalues and eigenvectors, diagonal representation. 5. Unitary linear operators. Selfadjoint linear operators. 6. Spectral representation. 7. Jordan normal form: Polynomial matrices and Jordan normal form. 8. Jordan normal form: JNF and invariant subspaces. 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces. 10. Tensors as linear operators, representation in bases, operations. 11. Algebraic structure of tensor spaces. 12. Exterior algebra. 13. Induced mappings of tensor spaces. 14. Physical applications-cartesian tensors.
- Literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Assessment methods (in Czech)
- Výuka: klasická prednáska, klasické cvičení. Zkouška: písemná (dvě části-(a) příklady, (b) test) a ústní.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2006
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D. - Timetable
- Mon 8:00–10:50 F1 6/1014
- Timetable of Seminar Groups:
F2182/02: Wed 12:00–12:50 B1,01004, M. Krbek, J. Musilová, P. Musilová - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Biophysics (programme PřF, M-FY)
- Physics (programme PřF, B-FY)
- Physics (programme PřF, M-FY)
- Physics (programme PřF, N-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics. Linear and multilinear algebra is one of most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important featuresand properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
- Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces. 2. Scalar product, orthogonalization, orthogonal projection. 3. Linear operators in vector spaces and their representation in bases. 4. Eigenvalues and eigenvectors, diagonal representation. 5. Unitary linear operators. Selfadjoint linear operators. 6. Spectral representation. 7. Jordan normal form: Polynomial matrices and Jordan normal form. 8. Jordan normal form: JNF and invariant subspaces. 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces. 10. Tensors as linear operators, representation in bases, operations. 11. Algebraic structure of tensor spaces. 12. Exterior algebra. 13. Induced mappings of tensor spaces. 14. Physical applications-cartesian tensors.
- Literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Assessment methods (in Czech)
- Výuka: klasická prednáska, klasické cvičení. Zkouška: písemná (dvě části-(a) příklady, (b) test) a ústní.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2005
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D. - Timetable
- Mon 8:00–10:50 F23-204
- Timetable of Seminar Groups:
F2182/02: Thu 12:00–12:50 F23-106, P. Musilová - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Biophysics (programme PřF, M-FY)
- Physics (programme PřF, B-FY)
- Physics (programme PřF, M-FY)
- Physics (programme PřF, N-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics. Linear and multilinear algebra is one of most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important featuresand properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
- Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces. 2. Scalar product, orthogonalization, orthogonal projection. 3. Linear operators in vector spaces and their representation in bases. 4. Eigenvalues and eigenvectors, diagonal representation. 5. Unitary linear operators. Selfadjoint linear operators. 6. Spectral representation. 7. Jordan normal form: Polynomial matrices and Jordan normal form. 8. Jordan normal form: JNF and invariant subspaces. 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces. 10. Tensors as linear operators, representation in bases, operations. 11. Algebraic structure of tensor spaces. 12. Exterior algebra. 13. Induced mappings of tensor spaces. 14. Physical applications-cartesian tensors.
- Literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Assessment methods (in Czech)
- Výuka: klasická prednáska, klasické cvičení. Zkouška: písemná (dvě části-(a) příklady, (b) test) a ústní.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2004
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jana Musilová, CSc. - Timetable of Seminar Groups
- F2182/01: No timetable has been entered into IS. P. Musilová
F2182/02: No timetable has been entered into IS. M. Krbek - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Biophysics (programme PřF, M-FY)
- Physics (programme PřF, B-FY)
- Physics (programme PřF, M-FY)
- Physics (programme PřF, N-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics. Linear and multilinear algebra is one of most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important featuresand properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
- Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces. 2. Scalar product, orthogonalization, orthogonal projection. 3. Linear operators in vector spaces and their representation in bases. 4. Eigenvalues and eigenvectors, diagonal representation. 5. Unitary linear operators. Selfadjoint linear operators. 6. Spectral representation. 7. Jordan normal form: Polynomial matrices and Jordan normal form. 8. Jordan normal form: JNF and invariant subspaces. 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces. 10. Tensors as linear operators, representation in bases, operations. 11. Algebraic structure of tensor spaces. 12. Exterior algebra. 13. Induced mappings of tensor spaces. 14. Physical applications-cartesian tensors.
- Literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Assessment methods (in Czech)
- Výuka: klasická prednáska, klasické cvičení. Zkouška: písemná (dvě části-(a) příklady, (b) test) a ústní.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2003
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jana Musilová, CSc. - Timetable of Seminar Groups
- F2182/01: No timetable has been entered into IS. M. Krbek, P. Musilová
F2182/02: No timetable has been entered into IS. M. Krbek, P. Musilová - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Biophysics (programme PřF, M-FY)
- Physics (programme PřF, B-FY)
- Physics (programme PřF, M-FY)
- Physics (programme PřF, N-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics. Linear and multilinear algebra is one of most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important featuresand properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
- Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces. 2. Scalar product, orthogonalization, orthogonal projection. 3. Linear operators in vector spaces and their representation in bases. 4. Eigenvalues and eigenvectors, diagonal representation. 5. Unitary linear operators. Selfadjoint linear operators. 6. Spectral representation. 7. Jordan normal form: Polynomial matrices and Jordan normal form. 8. Jordan normal form: JNF and invariant subspaces. 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces. 10. Tensors as linear operators, representation in bases, operations. 11. Algebraic structure of tensor spaces. 12. Exterior algebra. 13. Induced mappings of tensor spaces. 14. Physical applications-cartesian tensors.
- Literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Assessment methods (in Czech)
- Výuka: klasická prednáska, klasické cvičení. Zkouška: písemná (dvě části-(a) příklady, (b) test) a ústní.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2002
- Extent and Intensity
- 3/1/0. 5 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Plasma Physics and Technology – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jana Musilová, CSc. - Timetable of Seminar Groups
- F2182/01: No timetable has been entered into IS. P. Musilová
F2182/02: No timetable has been entered into IS. M. Krbek - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Biophysics (programme PřF, M-FY)
- Physics (programme PřF, B-FY)
- Physics (programme PřF, M-FY)
- Physics (programme PřF, N-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics. Linear and multilinear algebra is one of most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important featuresand properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
- Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces. 2. Scalar product, orthogonalization, orthogonal projection. 3. Linear operators in vector spaces and their representation in bases. 4. Eigenvalues and eigenvectors, diagonal representation. 5. Unitary linear operators. Selfadjoint linear operators. 6. Spectral representation. 7. Jordan normal form: Polynomial matrices and Jordan normal form. 8. Jordan normal form: JNF and invariant subspaces. 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces. 10. Tensors as linear operators, representation in bases, operations. 11. Algebraic structure of tensor spaces. 12. Exterior algebra. 13. Induced mappings of tensor spaces. 14. Physical applications-cartesian tensors.
- Literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Assessment methods (in Czech)
- Výuka: klasická prednáska, klasické cvičení. Zkouška: písemná (dvě části-(a) příklady, (b) test) a ústní.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2001
- Extent and Intensity
- 3/1/0. 5 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Zdeněk Bochníček, Dr.
Department of Plasma Physics and Technology – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jana Musilová, CSc. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Biophysics (programme PřF, M-FY)
- Physics (programme PřF, B-FY)
- Physics (programme PřF, M-FY)
- Physics (programme PřF, N-FY)
- Course objectives
- Fundamental course of linear and multilinear algebra for physicists. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces, scalar product, orthogonalization, orthogonal projection, linear operators in vector spaces and their representation in bases, eigenvalues and eigenvectors, diagonal representation, Jordan normal form, unitary linear operators, selfadjoint linear operators and spectral representation. Tensor algebra: dual space, dual basis, tensor product of vector spaces, tensors as linear operators, representation in bases, operations, algebraic structure of tensor spaces, exterior algebra, induced mappings of tensor spaces, physical applications-cartesian tensors.
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
The course is taught: every week.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2000
- Extent and Intensity
- 3/1/0. 5 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Zdeněk Bochníček, Dr.
Department of Plasma Physics and Technology – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jana Musilová, CSc. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Biophysics (programme PřF, M-FY)
- Physics (programme PřF, B-FY)
- Physics (programme PřF, M-FY)
- Physics (programme PřF, N-FY)
- Syllabus
- Fundamental course of linear and multilinear algebra for physicists. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces, scalar product, orthogonalization, orthogonal projection, linear operators in vector spaces and their representation in bases, eigenvalues and eigenvectors, diagonal representation, Jordan normal form, unitary linear operators, selfadjoint linear operators and spectral representation. Tensor algebra: dual space, dual basis, tensor product of vector spaces, tensors as linear operators, representation in bases, operations, algebraic structure of tensor spaces, exterior algebra, induced mappings of tensor spaces, physical applications-cartesian tensors.
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
The course is taught: every week.
F2182 Linear and multilinear algebra
Faculty of Sciencespring 2012 - acreditation
The information about the term spring 2012 - acreditation is not made public
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Michael Krbek, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics.
Linear and multilinear algebra is one of most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important featuresand properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
Absolving the discipline student obtains following kowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Selfadjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
The course is taught: every week.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2011 - only for the accreditation
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Michael Krbek, Ph.D. - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Biophysics (programme PřF, M-FY)
- Physics (programme PřF, B-FY)
- Physics (programme PřF, M-FY)
- Physics (programme PřF, N-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics.
Linear and multilinear algebra is one of most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important featuresand properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
Absolving the discipline student obtains following kowledge and skills:
* Deep understanding of the concept of linearity and linear mapping of vector spaces of general dimensions.
* Understanding of algebraic formulation of geometrical problems (general projection, etc.)
* Practical manipulations with linear mappings with the use of matrix calculus.
* Practical solution of eigenvalue problem for a linear operator, diagonalization.
* Understanding of the concept of a multilinear mapping and its applications in physics (tensor quantities).
* Practical calculus with tensors and tensor operations. - Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces.
- 2. Scalar product, orthogonalization, orthogonal projection.
- 3. Linear operators in vector spaces and their representation in bases.
- 4. Eigenvalues and eigenvectors, diagonal representation.
- 5. Unitary linear operators. Selfadjoint linear operators.
- 6. Spectral representation.
- 7. Jordan normal form: Polynomial matrices and Jordan normal form.
- 8. Jordan normal form: JNF and invariant subspaces.
- 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces.
- 10. Tensors as linear operators, representation in bases, operations.
- 11. Algebraic structure of tensor spaces.
- 12. Exterior algebra.
- 13. Induced mappings of tensor spaces.
- 14. Physical applications-cartesian tensors.
- Literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
The course is taught: every week.
F2182 Linear and multilinear algebra
Faculty of ScienceSpring 2008 - for the purpose of the accreditation
- Extent and Intensity
- 3/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Michael Krbek, Ph.D. - Prerequisites
- Fundamental knowledge of algebraic structures, fundamentals of matrix theory and their application for solving systems of linear equations.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Biophysics (programme PřF, M-FY)
- Physics (programme PřF, B-FY)
- Physics (programme PřF, M-FY)
- Physics (programme PřF, N-FY)
- Course objectives
- The discipline is a part of the fundamental course of linear and multilinear algebra for students of physics. Linear and multilinear algebra is one of most important mathematical tools, practically for all physical theories. Thus, the main goal of the discipline is to give to students a satisfactorily deep understanding of the concept of linear mapping and its fundamental properties. Only by such a way it is possible to ensure a good orientation of students in problems of vector and tensor algebra, the mathematically correct use of tensor calculus and the understanding of the most important featuresand properties of vector and tensor physical quantities. The discipline also gives a thorough preparation of algebraic tools for the theory of integration of forms on euclidean spaces and differential manifolds.
- Syllabus
- 1. Linear mappings of finite-dimensional vector spaces: representation of a vector in bases, subspaces. 2. Scalar product, orthogonalization, orthogonal projection. 3. Linear operators in vector spaces and their representation in bases. 4. Eigenvalues and eigenvectors, diagonal representation. 5. Unitary linear operators. Selfadjoint linear operators. 6. Spectral representation. 7. Jordan normal form: Polynomial matrices and Jordan normal form. 8. Jordan normal form: JNF and invariant subspaces. 9. Tensor algebra: dual space, dual basis. Tensor product of vector spaces. 10. Tensors as linear operators, representation in bases, operations. 11. Algebraic structure of tensor spaces. 12. Exterior algebra. 13. Induced mappings of tensor spaces. 14. Physical applications-cartesian tensors.
- Literature
- MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
- SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
- Assessment methods (in Czech)
- Výuka: klasická prednáska, klasické cvičení. Zkouška: písemná (dvě části-(a) příklady, (b) test) a ústní.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
The course is taught: every week.
- Enrolment Statistics (recent)