Linear Algebra Plus

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:

Syllabus of lectures:

Vector space -- linear independance, basis, dimension, subspace. Linear mapping (linear functional, linear operator) -- kernel, rank, defect, matrix of linear mapping. Dual space. Systems of linear algebraic equations -- Gauss elimination. Affine subspaces, convex sets.

Syllabus of tutorials:

1. Examples of vector spaces. 2. Investigation of linear dependence/independence, basis, coordinates -- problems with parameters (especially in vector spaces of polynomials, matrices etc.). 3. Selection of basis vectors from a set of generators, completing a basis from linearly independent vectors. 4. Intersection and sum of subspaces -- their basis and dimension. 5. Assembling matrices of linear mappings -- especially in spaces of polynomials, matrices etc. 6. Linear functionals -- dual basis. 7. Systems of linear algebraic equations including systems with parameters. 8. Geometry of linear manifolds, intersection and mutual position of affine subspaces, intersection of convex sets and various ways of their description.

Study Objective:

Knowledge: Basic concepts of linear algebra. Skills: To be able to use these findings in further studies not only of mathematical disciplines, but also in physics, economics etc.

Study materials:

Key references:

[1] Linear Algebra with Applications, Prentice-Hall, Inc., Englewood Cliffs, New Jersey,1980

[2] C. W. Curtis : Linear Algebra, An Introductory Approach, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo 1984.

Recommended references:

[3] P. Lancaster : Theory of Matrices, Academic Press, New York, London, 1969.

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 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)