## MUC31 Linear Algebra

Faculty of Science
Spring 2021
Extent and Intensity
2/2/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Josef Janyška, DSc. (lecturer)
Mgr. Petr Liška, Ph.D. (seminar tutor)
Bc. Kateřina Netrdová (assistant)
Bc. Jakub Sochor (assistant)
RNDr. Jan Vondra, Ph.D. (assistant)
Guaranteed by
prof. RNDr. Josef Janyška, DSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Timetable
Mon 1. 3. to Fri 14. 5. Wed 12:00–13:50 online_M1
• Timetable of Seminar Groups:
MUC31/01: Mon 1. 3. to Fri 14. 5. Tue 12:00–13:50 online_M5, P. Liška
MUC31/02: Mon 1. 3. to Fri 14. 5. Tue 18:00–19:50 online_M5, P. Liška
Prerequisites
! OBOR ( OM ) && ! OBOR ( STAT ) && ! OBOR ( FINPOJ ) && ! OBOR ( AMV ) && ! OBOR ( MOD )
High School Mathematics
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
Linear algebra belongs to basic mathematical education. Passing the course, the students should understand basic notions concerning vector spaces and linear maps and simultaneously they should have good computational skills with matrices and systems of linear equations.
Learning outcomes
The student will be able to:
- use coordinate to solve problems in vector spaces;
- solve problems in vector spaces with a scalar product;
- calculate the determinant of any square matrix;
- solve any system of linear equations;
- use the matrix.
Syllabus
• Vector spaces:
• - vector subspaces, linear span;
• - intersection and sum of vector subspaces;
• - linearly dependent and independent vectors;
• - basis and dimension of a vector space, coordinates of a vector.
• Matrices and determinants.
• Systems of linear equations.
• Euclidean vector spaces.
• Linear maps of vector spaces.
• Linear transformations and their matrices.
• Orthogonal mappings, orthogonal matrices.
Literature
recommended literature
• Náhradní obsah: Horák, Pavel. Lineární algebra a geometrie 1. Učební text. Jarní semestr 2017
• PASEKA, Jan and Pavol ZLATOŠ. Lineární algebra a geometrie I. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. URL info
• Exercises in algebra : a collection of exercises in algebra, linear algebra and geometry. Edited by Aleksej Ivanovič Kostrikin. Camberwell: Gordon and Breach Publishers, 1996. xii, 464 s. ISBN 2-88449-029-9. info
not specified
• BEČVÁŘ, Jindřich. Lineární algebra (Linear Algebra). Praha: MATFYZPRESS, 2000. 435 pp. ISBN 80-85863-61-8. info
Teaching methods
Lectures: theoretical explanations with examples of practical applications.
Exercises: solving problems focused on basic concepts and theorems, individual problem solving by students.
Assessment methods
Teaching: lectures, consultative exercises.
Exam: written and oral.
Current requirements: Written tests in exercises.
Language of instruction
Czech