Linear Algebra
Code  Completion  Credits  Range  Language 

BILIN  Z,ZK  7  4P+2C  Czech 
 Lecturer:
 Tutor:
 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:
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Information Technology  Version for those who Enrolled in 2012 (in Czech) (compulsory course in the program)
 Informatics (Bachelor) Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
 Web and Multimedia Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
 Computer Science  Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
 Information Technology  Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
 Software Engineering Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
 Information Systems and Management  Version for those who Enrolled in 2013 (in Czech) (compulsory course in the program)
 Informatics (Bachelor) Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
 Web and Multimedia Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
 Computer Science  Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
 Information Technology  Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
 Computer Engineering, Version for those who Enrolled in 2014, in Czech (compulsory course in the program)
 Software Engineering Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
 Information Systems and Management  Version for those who Enrolled in 2014 (in Czech) (compulsory course in the program)
 Bc. Programme Informatics, in Czech, Version 2015 to 2019 (compulsory course in the program)
 Bc. Branch Security and Information Technology, in Czech, Version 2015 to 2019 (compulsory course in the program)
 Bc. Branch Computer Science, in Czech, Version 2015 to 2019 (compulsory course in the program)
 Bc. Branch Computer Engineering, in Czech, Version 2015 to 2019 (compulsory course in the program)
 Bachelor Branch Information Systems and Management, in Czech, Version 2015 to 2019 (compulsory course in the program)
 Bachelor Branch Knowledge Engineering, in Czech, Version 2015, 2016 and 2017 (compulsory course in the program)
 Bachelor Branch WSI, Specialization Software Engineering, in Czech, Version 2015 to 2019 (compulsory course in the program)
 Bachelor Branch, Specialization Web Engineering, in Czech, Version 2015 to 2019 (compulsory course in the program)
 Bachelor Branch WSI, Specialization Computer Grafics, in Czech, Version 2015 to 2019 (compulsory course in the program)
 Bachelor Branch Knowledge Engineering, in Czech, Version 2015 to 2019 (compulsory course in the program)