Mathematics 3
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 finitedimensional 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:
 Timetable for winter semester 2019/2020:
 Timetable is not available yet
 Timetable for summer semester 2019/2020:
 Timetable is not available yet
 The course is a part of the following study plans:

 BS Aplikovaná informatika (compulsory course of the specialization)
 BS Jaderné inženýrství C (compulsory course of the specialization)
 BS Radiologická technika (compulsory course of the specialization)
 Bc Laser Technology and Instrumentation (compulsory course of the specialization)
 BS Fyzikální technika (compulsory course of the specialization)
 BS Jaderná chemie (compulsory course of the specialization)