Logo ČVUT
CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Linear Algebra Plus

The course is not on the list Without time-table
Code Completion Credits Range Language
01LAP Z,ZK 5 1+1 Czech
Grading of the course requires grading of the following courses:
Linear Algebra 1 (01LA1)
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:
Data valid to 2019-10-18
For updated information see http://bilakniha.cvut.cz/en/predmet24902105.html