Subject description - B0B01LAGA
Summary of Study |
Summary of Branches |
All Subject Groups |
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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:
Tento kurs pokrývá úvodní partie lineární algebry. Nejprve se studují základní pojmy související s prostorem a lineární transformací (lineární závislost a nezávislost vektorů, báze, souřadnice, atd.). Pak se přejde k otázkám maticového počtu (determinanty, inverzní matice, matice lineárního zobrazení, vlastní čísla a vlastní vektory, diagonalizace matice, atd.). Aplikace zahrnují řešení soustav lineárních rovnic, geometrii trojdimenzionálního prostoru (včetně skalárního a vektorového součinu) a SVD rozklad matice.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 |
| BPEK_2018 | Common courses | P | 1 |
| BPEEM2_2018 | Electrical Engineering and Management | P | 1 |
| BPEEM1_2018 | Applied Electrical Engineering | P | 1 |
| BPEEM_BO_2018 | Common courses | P | 1 |
| BPBIO_2018 | Common courses | P | 1 |
| Page updated 7.9.2024 12:51:27, semester: Z,L/2024-5, Z/2025-6, Z,L/2023-4, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |