Mathematics 3

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Code Completion Credits Range Language
01MAT3 Z,ZK 4 2+2 Czech
Garant předmětu:
David Krejčiřík
David Krejčiřík, Severin Pošta
David Krejčiřík, Severin Pošta
Department of Mathematics

The subject summarises the most important notions and theorems related to the study of finite-dimensional vector spaces.


Basic high school mathematics.

Syllabus of lectures:

1. Vector spaces;

2. Linear span and independence;

3. Basis and dimension;

4. Linear transformations;

5. Operator equations;

6. Scalar product and orthogonality;

7. Linear functionals and adjoint;

8. Matrices;

9. Determinants;

10. Spectrum;

11. Matrix exponential;

12. Quadratic forms.

Syllabus of tutorials:

0. Complex numbers;

1. Examples of vector spaces and subspaces;

2. Linear dependence of vectors - problem with parametres.

3. Selection of basis vectors from a set of generators, completing a basis;

4. Injectivity and kernel of a linear mapping;

5. Examples of scalar products and orthogonalization process;

6. Examples of linear functionals and construction of adjoint mappings;

7. Operations with matrices and construction of the matrix of a linear mapping;

8. Working with determinants, computation of the inverse matrix;

9. Eigenvalues and eigenfunctions of matrices;

10. Construction of matrix exponential;

11. Properties of quadratic forms.

Study Objective:

Knowledge: Learning basic concepts of linear algebra necessary for a proper understanding of related subjects, such as analysis of functions of several variables, numerical mathematics, and so on. Skills: Applications of theoretical concepts and theorems in continuing subjects.

Study materials:

Key references:

[1] S. Axler: Linear algebra done right, Springer, New York 2014

Recommended references:

[2] J. Kopáček, Matematika pro fyziky II, UK, Praha, 1989.

[3] Lecture notes on the hompeage of the lecturer.

Time-table for winter semester 2023/2024:
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Time-table for summer semester 2023/2024:
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The course is a part of the following study plans:
Data valid to 2024-04-23
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