MUC31 Linear Algebra

Faculty of Science
Spring 2026
Extent and Intensity
2/2/0. 4 credit(s). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
prof. RNDr. Josef Janyška, DSc. (lecturer)
Mgr. Pavel Francírek, Ph.D. (seminar tutor)
RNDr. Jakub Novák (seminar tutor)
Tomáš Ficnar (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 16. 2. to Fri 22. 5. Tue 16:00–17:50 M1,01017
  • Timetable of Seminar Groups:
MUC31/01: Mon 16. 2. to Fri 22. 5. Wed 8:00–9:50 M4,01024, P. Francírek
MUC31/02: Mon 16. 2. to Fri 22. 5. Wed 12:00–13:50 M4,01024, P. Francírek
MUC31/03: Mon 16. 2. to Fri 22. 5. Thu 14:00–15:50 M5,01013, J. Novák
Prerequisites
!OBOR(OM) && !OBOR(STAT) && !OBOR(FINPOJ) && !OBOR(AMV) && !OBOR(MOD)
High School Mathematics and MUC03
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
there are 7 fields of study the course is directly associated with, display
Abstract
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.
Key topics
  • 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.
Study resources and literature
    recommended literature
  • Janyška, Josef, Lineární algebra, učební text MU, on-line 2025.
  • PASEKA, Jan and Pavol ZLATOŠ. Lineární algebra a geometrie I. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. URL info
  • BEČVÁŘ, Jindřich. Lineární algebra (Linear Algebra). Praha: MATFYZPRESS, 2000, 435 pp. ISBN 80-85863-61-8. 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
  • STRANG, Gilbert. Introduction to linear algebra. 4th ed. Wellesley, MA: Wellesley-Cambridge Press, 2009, ix, 574. ISBN 9780980232721. info
  • LARSON, Ron and David C. FALVO. Elementary linear algebra. 6th ed. Belmont: Brooks/Cole, 2010, xvi, 480. ISBN 9780495829232. info
  • POOLE, David. Linear algebra : a modern introduction. Fourth edition. Stamford: Cengage Learning, 2015, xxiv, 619. ISBN 9781285463247. info
    not specified
  • BICAN, Ladislav. Lineární algebra a geometrie. Vyd. 2. Praha: Academia, 2009, 303 s. ISBN 9788020017079. info
Approaches, practices, and methods used in teaching
Lectures: theoretical explanations with examples of practical applications.
Exercises: solving problems focused on basic concepts and theorems, individual problem solving by students.
Method of verifying learning outcomes and course completion requirements
Teaching: lectures, consultative exercises.
Exam: written and oral.
Current requirements: Written tests in exercises.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~janyska
The course is also listed under the following terms Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2026/MUC31