Linear Algebra
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| BI-LIN | 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 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:
- Further information:
- https://courses.fit.cvut.cz/BI-LIN/
- Time-table for winter semester 2023/2024:
- Time-table is not available yet
- Time-table for summer semester 2023/2024:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Bachelor program Informatics, unspecified branch, in Czech, 2015-2020 (compulsory course in the program)
- Bachelor branch Security and Information Technology, in Czech, 2015-2020 (compulsory course in the program)
- Bachelor branch Computer Science, in Czech, 2015-2020 (compulsory course in the program)
- Bachelor branch Computer Engineering, in Czech, 2015-2020 (compulsory course in the program)
- Bachelor branch Information Systems and Management, in Czech, 2015-2020 (compulsory course in the program)
- Bachelor branch Web and Software Engineering, spec. Software Engineering, in Czech, 2015-2020 (compulsory course in the program)
- Bachelor branch Web and Software Engineering, spec. Web Engineering, in Czech, 2015-2020 (compulsory course in the program)
- Bachelor branch Web and Software Engineering, spec. Computer Graphics, in Czech, 2015-2020 (compulsory course in the program)
- Bachelor branch Knowledge Engineering, in Czech, 2018-2020 (compulsory course in the program)
During a review of study plans, the course BI-LA1.21 can be substituted for the course BI-LIN.