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PřF:MUC31 Linear Algebra - Course Information

## MUC31 Linear Algebra

**Faculty of Science**

Spring 2022

**Extent and Intensity**- 2/2/0. 4 credit(s). Type of Completion: zk (examination).

Taught in person. **Teacher(s)**- prof. RNDr. Josef Janyška, DSc. (lecturer)

Mgr. Petr Liška, Ph.D. (seminar tutor)

Bc. Kateřina Netrdová (assistant)

Bc. Jakub Sochor (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 **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**- there are 7 fields of study the course is directly associated with, display
**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**- 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

*recommended literature*- BEČVÁŘ, Jindřich.
*Lineární algebra (Linear Algebra)*. Praha: MATFYZPRESS, 2000. 435 pp. ISBN 80-85863-61-8. info

*not specified***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
**Further Comments**- The course is taught annually.

The course is taught: every week. **Teacher's information**- http://www.math.muni.cz/~janyska

- Enrolment Statistics (Spring 2022, recent)
- Permalink: https://is.muni.cz/course/sci/spring2022/MUC31