Linear Algebra

The course cannot be taken simultaneously with:

Linear Algebra (A8B01LAG)
Linear Algebra (B0B01LAG)

Garant předmětu:

Jiří Velebil

Lecturer:

Jiří Velebil

Tutor:

Matěj Dostál, Daria Dunina, Josef Dvořák, Karel Pospíšil, Vladimír Puš, Jiří Velebil, Natalie Žukovec

Supervisor:

Department of Mathematics

Synopsis:

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 2023/2024:

	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	roomT4:D2-256 Velebil J. 16:15–17:45 (lecture parallel1) Dejvice Posluchárna 256
Tue	roomT2:C3-52 Puš V. 14:30–16:00 (lecture parallel1 parallel nr.122) Dejvice T2:C3-52roomT2:C3-52 18:00–19:30 (lecture parallel1 parallel nr.108) Dejvice T2:C3-52 roomT2:C3-52 Puš V. 16:15–17:45 (lecture parallel1 parallel nr.121) Dejvice T2:C3-52roomT2:C3-52 18:00–19:30 (lecture parallel1 parallel nr.123) Dejvice T2:C3-52
Wed	roomT2:A4-204 11:00–12:30 (lecture parallel1 parallel nr.101) Dejvice UčebnaroomT2:A4-204 12:45–14:15 (lecture parallel1 parallel nr.103) Dejvice UčebnaroomT2:A4-204 14:30–16:00 (lecture parallel1 parallel nr.111) Dejvice UčebnaroomT2:C3-52 16:15–17:45 (lecture parallel1 parallel nr.114) Dejvice T2:C3-52 room 11:00–12:30 (lecture parallel1 parallel nr.106) roomT2:C4-78 12:45–14:15 (lecture parallel1 parallel nr.105) Dejvice T2:C4-78roomT2:C4-78 14:30–16:00 (lecture parallel1 parallel nr.116) Dejvice T2:C4-78
Thu	roomT2:A4-202b 12:45–14:15 (lecture parallel1 parallel nr.104) Dejvice UčebnaroomT2:A4-202a 14:30–16:00 (lecture parallel1 parallel nr.102) Dejvice Ucebnaroom 16:15–17:45 (lecture parallel1 parallel nr.107) roomT2:A4-204 Puš V. 14:30–16:00 (lecture parallel1 parallel nr.112) Dejvice UčebnaroomT2:A4-204 Puš V. 16:15–17:45 (lecture parallel1 parallel nr.113) Dejvice Učebna roomT2:A4-203a 14:30–16:00 (lecture parallel1 parallel nr.115) Dejvice UčebnaroomT2:C2-82 16:15–17:45 (lecture parallel1 parallel nr.120) Dejvice T2:C2-82
Fri	roomT2:D3-309 Velebil J. 11:00–12:30 (lecture parallel1) Dejvice T2:D3-309 roomT2:D3-209 Velebil J. 11:00–12:30 (lecture parallel1) Dejvice T2:D3-209

Time-table for summer semester 2023/2024:

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)