Linear Algebra
Code  Completion  Credits  Range  Language 

BILIN  Z,ZK  7  4P+2C  Czech 
 Garant předmětu:
 Daniel Dombek
 Lecturer:
 Daniel Dombek
 Tutor:
 Daniel Dombek
 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 errordetecting and errorcorrecting 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. Selfcorrecting 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 errordetecting and errorcorrecting 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. Selfcorrecting 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:
 Further information:
 https://courses.fit.cvut.cz/BILIN/
 Timetable for winter semester 2023/2024:
 Timetable is not available yet
 Timetable for summer semester 2023/2024:
 Timetable is not available yet
 The course is a part of the following study plans:

 Bachelor program Informatics, unspecified branch, in Czech, 20152020 (compulsory course in the program)
 Bachelor branch Security and Information Technology, in Czech, 20152020 (compulsory course in the program)
 Bachelor branch Computer Science, in Czech, 20152020 (compulsory course in the program)
 Bachelor branch Computer Engineering, in Czech, 20152020 (compulsory course in the program)
 Bachelor branch Information Systems and Management, in Czech, 20152020 (compulsory course in the program)
 Bachelor branch Web and Software Engineering, spec. Software Engineering, in Czech, 20152020 (compulsory course in the program)
 Bachelor branch Web and Software Engineering, spec. Web Engineering, in Czech, 20152020 (compulsory course in the program)
 Bachelor branch Web and Software Engineering, spec. Computer Graphics, in Czech, 20152020 (compulsory course in the program)
 Bachelor branch Knowledge Engineering, in Czech, 20182020 (compulsory course in the program)
During a review of study plans, the course BILA1.21 can be substituted for the course BILIN.