Linear Algebra I - NOFY141
Title: Lineární algebra I
Guaranteed by: Laboratory of General Physics Education (32-KVOF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Additional information:
Guarantor: Mgr. Dalibor Šmíd, Ph.D.
prof. Ing. Branislav Jurčo, CSc., DSc.
Mgr. Lukáš Krump, Ph.D.
Class: Fyzika
Classification: Mathematics > Algebra
Physics > Mathematics for Physicists
Incompatibility : NMAF027
Interchangeability : NMAF027
Is incompatible with: NMAF027
Is interchangeable with: NMAF027
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Annotation -
Last update: Mgr. Hana Kudrnová (20.05.2019)
This course gives, together with parallel courses on analysis, a basic course of mathematics for physicists. Emphasis is given also to relationship of all these disciplines. Keywords linear spaces, dimension, matrices, determinants, groups and algebras of matrices, eigenvalues, Jordan normal form.
Course completion requirements -
Last update: Mgr. Lukáš Krump, Ph.D. (16.10.2023)

Available on the webpage of the course

Literature -
Last update: Mgr. Dalibor Šmíd, Ph.D. (28.09.2020)

D. Šmíd: Lineární algebra pro fyziky, elektronic scriptum, available on the webpage of the course

K. Výborný, M.Zahradník: Používáme lineární algebru (sbírka řešených příkladů), Karolinum 2002

Other sources available on the webpageof the course.

Requirements to the exam -
Last update: Mgr. Dalibor Šmíd, Ph.D. (28.09.2020)

Available on the webpage of the course

Syllabus -
Last update: Mgr. Dalibor Šmíd, Ph.D. (28.09.2020)

1 Systems of linear equations, Gauss elimination method.

2 Matrix operations, inversion of a matrix.

3 Groups, vector spaces. Subspaces, linear independence, linear span.

4 Basis, dimension, Steinitz theorem.

5 Rank of a matrix, Frobenius theorem.

6 Linear maps and their matrices, kernel and image, rank-nullity theorem.

7 Coordinates and their transformations, similarity of matrices, trace of a matrix and of a linear map.

8 Scalar product, Cauchy-Schwarz inequality.

9 Orthogonal complement, orthogonal projection.

10 Permutation and its sign.

11 Determinant and its properties. Expansion along a row and a column.

12 Determinant of a product, inverse matrix formula, Cramer's rule.

13 Eigenvectors and eigenspaces.

14 Block matrices, sum and direct sum of subspaces.