MUC31 Linear Algebra

Faculty of Science
Spring 2023
Extent and Intensity
2/2/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Josef Janyška, DSc. (lecturer)
RNDr. Iva Dřímalová, Ph.D. (seminar tutor)
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
Thu 16:00–17:50 M1,01017
  • Timetable of Seminar Groups:
MUC31/01: Fri 8:00–9:50 M5,01013, I. Dřímalová
MUC31/02: Fri 12:00–13:50 M5,01013, I. Dřímalová
MUC31/03: Fri 10:00–11:50 M5,01013, I. Dřímalová
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
    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
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 2024, Spring 2025.
  • Enrolment Statistics (Spring 2023, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2023/MUC31