Linear Algebra
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| B0B01LAG | Z,ZK | 8 | 4P+2S | Czech |
- The course cannot be taken simultaneously with:
- Linear Algebra (A8B01LAG)
Linear Algebra (B0B01LAGA) - The course is a substitute for:
- Linear Algebra (B0B01LAGA)
- Garant předmětu:
- Jiří Velebil
- Lecturer:
- Jiří Velebil
- Tutor:
- Matěj Dostál, Josef Dvořák, Daniel Gromada, Dominik Krasula, Matouš Pikous, Karel Pospíšil, Jiří Velebil
- Supervisor:
- Department of Mathematics
- Synopsis:
-
The course covers the initial parts of linear algebra. Firstly, the basic notions of a linear space and linear mappings are covered (linear dependence and independence, basis, coordinates, etc). The calculus of matrices (determinants, inverse matrices, matrices of a linear map, eigenvalues and eigenvectors, diagonalisation, etc) is covered next. The applications include solving systems of linear equations, the geometry of a 3D space (including the scalar product and the vector product) and SVD.
- Requirements:
- Syllabus of lectures:
-
1. Linear spaces.
2. Linear span, linear dependence and independence.
3. Basis, dimensions, coordinates w.r.t. a basis.
4. Linear mappings, matrices as linear mappings.
5. The matrix of a linear mapping, transformatio of coordinates.
6. Systems of linear equations, Frobenius' Theorem, geometry of solutions of systems.
7. The determinant of a square matrix.
8. Eigenvalues and diagonalisation, Jordan's form.
9. The abstract scalar product.
10. Orthogonal projections and orthogonalisation.
11. Least squares, SVD and pseudoinverse.
12. Mutual position of affine subspaces and their mutual distance.
13. Vector product and metric calculations in R^n.
14. Spare week.
- Syllabus of tutorials:
- Study Objective:
- Study materials:
-
[1] Halmos, P.: Finite-dimensional vector spaces,2nd edition, Springer 2000.
[2] Strang, G.: Introduction to linear algebra, 5th edition, Wellesley-Cambridge 2016.
- Note:
- Further information:
- https://moodle.fel.cvut.cz/courses/B0B01LAG
- Time-table for winter semester 2022/2023:
-
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri - Time-table for summer semester 2022/2023:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Electrical Engineering, Power Engineering and Management - Applied Electrical Engineering 2016 (compulsory course in the program)
- Electrical Engineering, Power Engineering and Management - Electrical Engineering and Management (compulsory course in the program)
- Cybernetics and Robotics 2016 (compulsory course in the program)
- Open Informatics - Computer Science 2016 (compulsory course in the program)
- Open Informatics - Internet of Things 2016 (compulsory course in the program)
- Open Informatics - Software 2016 (compulsory course in the program)
- Open Informatics - Computer Games and Graphics 2016 (compulsory course in the program)
- Electrical Engineering, Power Engineering and Management (compulsory course in the program)
- Open Informatics (compulsory course in the program)
- Open Informatics (compulsory course in the program)
- Open Informatics - Artificial Intelligence and Computer Science 2018 (compulsory course in the program)
- Open Informatics - Internet of Things 2018 (compulsory course in the program)
- Open Informatics - Software 2018 (compulsory course in the program)
- Open Informatics - Computer Games and Graphics 2018 (compulsory course in the program)
- Cybernetics and Robotics 2016 (compulsory course in the program)