Linear Algebra
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| B0B01LAGA | Z,ZK | 7 | 4P+2S | Czech |
- Relations:
- It is not possible to register for the course B0B01LAGA if the student is concurrently registered for or has already completed the course B0B01LAG (mutually exclusive courses).
- It is not possible to register for the course B0B01LAGA if the student is concurrently registered for or has already completed the course A8B01LAG (mutually exclusive courses).
- It is not possible to register for the course B0B01LAGA if the student is concurrently registered for or has previously completed the course B0B01LAG (mutually exclusive courses).
- The requirement for course B0B01LAGA can be fulfilled by substitution with the course BE5B01LAL.
- The requirement for course B0B01LAGA can be fulfilled by substitution with the course B0B01LAG.
- Course guarantor:
- Jiří Velebil
- Lecturer:
- Jiří Velebil
- Tutor:
- Martin Bohata, Matěj Dostál, Josef Dvořák, Alena Gollová, Daniel Gromada, Jakub Rondoš, Jiří Velebil, Natalie Žukovec
- Supervisor:
- Department of Mathematics
- Synopsis:
-
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.
- 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.
- Note:
- Further information:
- https://moodle.fel.cvut.cz/courses/B0B01LAGA
- Time-table for winter semester 2024/2025:
-
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 2024/2025:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Medical electronics and bioinformatics (compulsory course in the program)
- Electronics and Communications 2018 (compulsory course in the program)
- Electrical Engineering, Power Engineering and Management (compulsory course in the program)
- Electrical Engineering, Power Engineering and Management - Applied Electrical Engineering 2018 (compulsory course in the program)
- Electrical Engineering, Power Engineering and Management - Electrical Engineering and Management (compulsory course in the program)