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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Mathematics 3

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Code Completion Credits Range Language
01MAT3 Z,ZK 4 2+2 Czech
Lecturer:
David Krejčiřík (guarantor)
Tutor:
David Krejčiřík (guarantor)
Supervisor:
Department of Mathematics
Synopsis:

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

Requirements:

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.

Note:
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2019-10-18
For updated information see http://bilakniha.cvut.cz/en/predmet11278305.html