Subject description - B0B01LAGA
Summary of Study |
Summary of Branches |
All Subject Groups |
All Subjects |
List of Roles |
Explanatory Notes
Instructions
| B0B01LAGA | Linear Algebra | ||
|---|---|---|---|
| Roles: | P | Extent of teaching: | 4P+2S |
| Department: | 13101 | Language of teaching: | CS |
| Guarantors: | Velebil J. | Completion: | Z,ZK |
| Lecturers: | Velebil J. | Credits: | 7 |
| Tutors: | Too many persons | Semester: | Z |
Web page:
https://moodle.fel.cvut.cz/courses/B0B01LAGAAnotation:
The course covers introductory topics of linear algebra. It begins with fundamental concepts related to vector spaces and linear transform (such as linear dependence and independence of vectors, bases, coordinates of vectors, etc.). The next part of the course is devoted to matrix theory (determinants, inverse matrix, matrices of linear transformation, eigenvalues and eigenvectors). Applications include solving systems of linear equations, geometry in three-dimensional space (including dot and cross products), and the singular value decomposition of a matrix.Course outlines:
| 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. |
Exercises outline:
Literature:
| [1] | Halmos, P.: Finite-dimensional vector spaces,2nd edition, Springer 2000. |
Requirements:
Subject is included into these academic programs:| Program | Branch | Role | Recommended semester |
| BPEEM_BO_2018 | Common courses | P | 1 |
| BPEEM2_2018 | Electrical Engineering and Management | P | 1 |
| BPEEM1_2018 | Applied Electrical Engineering | P | 1 |
| BPBIO_2018 | Common courses | P | 1 |
| BPEK_2018 | Common courses | P | 1 |
| BPEK_2026 | Common courses | P | 1 |
| BPEEM2_2026 | Electrical Engineering and Management | P | 1 |
| BPBIO_2026 | Common courses | P | 1 |
| BPEEM_BO_2026 | Common courses | P | 1 |
| BPEEM1_2026 | Applied Electrical Engineering | P | 1 |
| Page updated 13.8.2026 17:50:46, semester: L/2029-30, Z/2027-8, L/2028-9, L/2026-7, L/2025-6, Z/2026-7, Z/2028-9, L/2027-8, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |