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)
- Lecturer:
- Jiří Velebil (guarantor)
- Tutor:
- Jiří Velebil (guarantor), Dominik Beck, Matěj Dostál, Daria Dunina, Josef Dvořák, Daniel Gromada, Karel Pospíšil, Paola Vivi, Jana Vráblíková
- 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. Intro, polynomials.
2. Linear spaces, linear dependence and independence.
3. Basis, dimensions, coordinates w.r.t. a basis.
4. Matrices, algebra of matrices, determinants. Inverse of a matrix.
5. Systems of linear equations.
6. The description of solutions of homogeneous and inhomogeneous systems of linear equations.
7. Linear mappings. The matrix of a linear mapping.
8. The scalar and the vector product.
9. Applications of scalar product and vector product.
10. The Gram-Schmidt orthogonalisation, orthogonal projections.
11. Eigen vectors and eigenvalues of matrices and linear mappings.
12. Similarity of matrices, diagonalisation, (an outline of) Jordan form.
13. SVD and Moore-Penrose pseudoinverse.
14. Reserve 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 2021/2022:
-
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 2021/2022:
- 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)