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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2018/2019

Linear Algebra

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Code Completion Credits Range Language
BI-LIN Z,ZK 7 4+2 Czech
Lecturer:
Daniel Dombek (guarantor), Luděk Kleprlík
Tutor:
Daniel Dombek (guarantor), Matyáš Hollmann, Tomáš Kalvoda, Luděk Kleprlík, Petr Matyáš, Marta Nollová, Petr Pauš, Ivo Petr, Jitka Rybníčková, Iveta Semorádová, Jiřina Scholtzová, Jan Starý, Lucie Strmisková, František Štampach, Jakub Tichý (Štěpán)
Supervisor:
Department of Applied Mathematics
Synopsis:

The course is taught in Czech.

Students understand the theoretical foundation of algebra and mathematical principles of linear models of systems around us, where the dependencies among components are only linear. They know the basic methods for operating with matrices and linear spaces. They are able to perform matrix operations and solve systems of linear equations. They can apply these mathematical principles to solving problems in 2D or 3D analytic geometry. They understand the error-detecting and error-correcting codes.

Requirements:

Secondary school mathematics.

Syllabus of lectures:

Course lectures is taught in Czech.

1. Polynomials, roots of polynomials, irreducible polynomials. Polynomials in R, C, Q.

2. Sets of linear equations. Gaussian elimination method.

3. Linear spaces, axiomatic definition.

4. Linear combination and linear independence.

5. Bases, dimensions, vector coordinates in a base.

6. Linear maps (homomorphism, isomorphism), kernel, defect, composition of maps.

7. Matrices, matrix operations.

8. Determinants.

9. Inverse matrix, its calculation.

10. Matrix of homomorphism. Rotation, projection onto a straight line (plane), symmetry with respect to a straight line (plane) in R^2, R^3. Transformation of coordinates.

11. Eigenvalues and eigenvectors of a matrix or a linear map.

12. Scalar product, orthogonality. Euclidean and unitary space. Linear map of Euclidean and unitary spaces. Affine space. Affine transformation. Translation.

13. Group, ring, field. Properties of a field. Finite fields.

14. Self-correcting codes.

Syllabus of tutorials:

The course seminary is taught in Czech.

Students understand the theoretical foundation of algebra and mathematical principles of linear models of systems around us, where the dependencies among components are only linear. They know the basic methods for operating with matrices and linear spaces. They are able to perform matrix operations and solve systems of linear equations. They can apply these mathematical principles to solving problems in 2D or 3D analytic geometry. They understand the error-detecting and error-correcting codes.

1. Operations with polynomials. Roots of polynomials.

2. Sets of linear equations. Gaussian elimination method.

3. Linear dependence and independence.

4. Bases, dimensions, vector coordinates in a base. Coordinate transformations.

5. Matrices, matrix operations.

6. Determinants and their calculation.

7. Inverse matrix and its calculation.

8. Sets of linear equations. Cramer's Theorem.

9. Linear map, linear map matrix.

10. Eigenvalues and eigenvectors of a matrix.

11. Scalar product, orthogonality.

12. Affine transformation. Translation.

13. Group, ring, field. Properties of a field. Finite fields.

14. Self-correcting codes.

Study Objective:

The course is taught in Czech.

The goal of the module is to build basic mathematical way of thinking and provide students

Study materials:

The course is taught in Czech.

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

Note:
Time-table for winter semester 2018/2019:
Time-table is not available yet
Time-table for summer semester 2018/2019:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2018-11-15
For updated information see http://bilakniha.cvut.cz/en/predmet1121206.html