Linear Algebra 1

Lecturer:

Lubomíra Balková (gar.), Emil Humhal

Tutor:

Lubomíra Balková (gar.), Jiří Franc, Emil Humhal, Dalibor Karásek, Jiří Pytlíček, Jan Starý, Jakub Železný

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. A vector space

2. linear dependence and independence

3. basis and dimension

4. subspaces of a vector space

5. linear transformations

6. matrices

7. matrices of linear transformations

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 - problems with parameters.

4. Selection of basis vectors from a set of generators, completing a basis.

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

6. Assembling matrices of 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:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: