Logo ČVUT
CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2018/2019

Linear Algebra

The course is not on the list Without time-table
Code Completion Credits Range Language
A7B01LAG Z,ZK 6 2+2 Czech
The course cannot be taken simultaneously with:
Introduction to Algebra (Y01ALG)
The course is a substitute for:
Introduction to Algebra (Y01ALG)
Lecturer:
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

The course covers introductory topics of linear algebra. They include matrices, matrix operations, inversion of matrices, vector spaces, bases and dimension and their applications to solving systems of linear equations. Vector spaces are presented over real numbers and GF(2). Eigenvalues and eigenvectors of matrices.

Requirements:

To be specified in seminars by tutors.

Syllabus of lectures:

1. Vector spaces, axioms of linearity.

2. Linear independence, linear dependence, linear span.

3. Basis, dimension, coordinates of vectors.

4. Matrices, operations with matrices.

5. Determinants.

6. Inverse matrices.

7. Systems of linear equations.

8. Linear mappings, matrices of linear mappings.

9. Eigenvalues and eigenvectors of matrices.

10. Scalar product, orthogonality.

11. Arithmetic vectors over GF(2), solution of linear equations over FG(2).

12. Applications in linear coding.

13. Back-up class.

Syllabus of tutorials:

1. Polynomials, roots of polynomials.

2. Gaussian elimination, rank of matrices.

3. Vector spaces, linear independence, linear dependence.

4. Basis, dimension, coordinates of vectors.

5. Matrices, operations with matrices.

6. Determinants.

7. Systems of linear equations.

8. Linear mappings, matrices of linear mappings.

9. Eigenvalues and eigenvectors of matrices.

10. Scalar product, orthogonality.

11. Arithmetic vectors over GF(2), solution of linear equations over FG(2).

12. Applications in linear coding.

13. Back-up class.

Study Objective:
Study materials:

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

2. P. Pták: Introduction to Linear Algebra, starší vydání přístupné elektronicky.

Note:
Further information:
http://math.feld.cvut.cz/velebil/teaching/a7b01lag.html
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2019-06-16
For updated information see http://bilakniha.cvut.cz/en/predmet1389806.html