CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Linear Algebra

The course is not on the list Without time-table
Code Completion Credits Range Language
AE0B01LAG Z,ZK 7 4+2
Lecturer:
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

This course covers introductory topics of linear algebra. The main focus

is on

the related notions of linear spaces and linear transformations (linear

independence, bases and coordinates) and matrices (determinants, inverse

matrix, matrix of a linear mapping, eigenvalues). Applications include

solving systems of linear equations, geometry in 3-space (including dot

product and cross product), and solving linear differential equations.

Requirements:
Syllabus of lectures:

1. Introduction, polynomials.

2. Linear spaces, linear dependence and independence.

3. Basis, dimension, coordinates of vectors.

4. Matrices, operations, determinants. Inverse matrix.

5. Systems of linear equations.

6. Linear mappings. Matrix of a linear mapping.

7. Free vectors. Dot product and cross product.

8. Lines and planes in 3-dimensional Euclidean space.

9. Eigenvalues and eigenvectors of matrices and linear mappings.

10. Similarity of matrices, matrices similar to diagonal matrices.

11. Generalized eigenvectors.

12. Systems of linear differential equations of 1st order with constant coefficients.

13. Linear differential equations of order n with constant coefficients.

14. Back-up class.

Syllabus of tutorials:

1. Polynomials.

2. Examples of linear spaces, linear independence.

3. Basis, coordinates of vectors.

4. Operations with matrices, determinants. Finding inverse matrix.

5. Systems of linear equations.

6. Examples of linear mappings.

7. Matrix of a linear mapping, change of basis.

8. Dot product and cross product in geometry. Lines and planes.

9. Eigenvalues and eigenvectors of matrices.

10. Diagonalization of matrices.

11. Generalized eigenvectors and applications.

12. Systems of linear differential equations.

13. Linear differential equations of order n.

14. Back-up class.

Study Objective:
Study materials:

[1] P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 2005.

Note:
Further information:
http://math.feld.cvut.cz/vivi/
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2020-01-18
For updated information see http://bilakniha.cvut.cz/en/predmet12773204.html