Linear Algebra 1

Garant předmětu:

Lubomíra Dvořáková

Lecturer:

Lubomíra Dvořáková

Tutor:

Petr Ambrož, Marek Dědič, Lubomíra Dvořáková, Miroslav Kolář, Václav Košík, David Kramár, David Krejčiřík, Romana Kvasničková, Martin Malachov, Jiří Mikyška, Rudolf Šmolka

Supervisor:

Department of Mathematics

Synopsis:

1. Vector space.

2. Linear dependence and independence.

3. Basis and dimension.

4. Subspaces of vector spaces.

5. Linear mappings.

6. Matrices of linear mappings.

7. Frobenius theorem.

Requirements:

Just basic highschool mathematics knowledge is demanded.

Syllabus of lectures:

1. Vector space

2. Linear (in)dependance

3. Basis and dimension

4. Subspace

5. Linear mapping

6. Matrix of linear mapping

7. Frobenius theorem

Syllabus of tutorials:

1. Vector space / examples

2. Linear dependence and independence.

3. Calculation of vector-space dimension.

4. Subspaces of vector spaces and spans.

5. Linear mappings and matrix composition. Mapping operations.

7. Solution of linear algebraic equation systems.

Study Objective:

Study materials:

Key references:

[1] L. Dvořáková: Linear algebra 1, textbook, accessible online on demand

[2] T. M. Apostol: Linear Algebra: A First Course with Applications to Differential Equations, John Wiley & Sons, 2014

[3] R. C. Penney: Linear algebra and applications, John Wiley &Sons, 2015

Recommended references:

[3] G. Strang: Introduction to Linear Algebra, Wesley – Cambridge Press, 2016

Note:

Time-table for winter semester 2022/2023:

Time-table is not available yet

Time-table for summer semester 2022/2023:

Time-table is not available yet

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 Matematická informatika (compulsory course of the specialization)
• 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)
• Bc Laser Technology and Instrumentation (compulsory course of the specialization)
• Applications of Informatics in Natural Sciences (compulsory course in the program)