Linear Algebra 1

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The subject summarizes the most important notions and theorems related to the study of vector spaces.

Requirements:

Basic high school mathematics

Syllabus of lectures:

1. Vector space

2. Linear dependence and independence

3. Basis and dimension

4. Subspaces of a vector space

5. Linear transformations

6. Matrices of linear transformations

7. Frobenius theorem

Syllabus of tutorials:

1. Basic information on solution of systems of linear algebraic equations.

2. Examples of vector spaces.

3. Investigation of linear dependence/independence, basis, coordinates.

4. Selection of basis vectors from a set of generators, completion of a basis from linearly independent vectors.

5. Intersection and sum of subspaces -- their basis and dimension.

6. Assembling matrices of linear mapping.

7. Solution of equations for linear mapping.

Study Objective:

Knowledge:

Basic concepts of linear algebra necessary for a proper understanding of related subjects, such as analysis of functions of several variables, numerical mathematics.

Skills:

Applications of theoretical notions and theorems in continuing subjects.

Study materials:

Key references:

[4] C. W. Curtis: Linear Algebra, An Introductory Approach. Springer-Verlag 1984

Recommended references:

[5] Faddeev D. K., Faddeeva V. N.: Computional Methods of Linear Algebra. Freeman, San Francisko, London 1963

Note:

Further information:

http://kmlinux.fjfi.cvut.cz/~balkolub/vyuka.html

No time-table has been prepared for this course

The course is a part of the following study plans:

• BS Matematické inženýrství - Matematické modelování (compulsory course of the specialization)
• BS Matematické inženýrství - Matematická fyzika (compulsory course of the specialization)
• BS Matematické inženýrství - Aplikované matematicko-stochastické metody (compulsory elective course)
• BS Informatická fyzika (compulsory elective course)
• BS Aplikace softwarového inženýrství (compulsory course of the specialization)
• BS jaderné inženýrství B (compulsory course of the specialization)
• BS Dozimetrie a aplikace ionizujícího záření (compulsory elective course)
• BS Experimentální jaderná a částicová fyzika (compulsory elective course)
• BS Inženýrství pevných látek (compulsory elective course)
• BS Diagnostika materiálů (compulsory elective course)
• BS Fyzika a technika termojaderné fúze (compulsory elective course)
• BS Fyzikální elektronika (compulsory elective course)