Linear Algebra

Code	Completion	Credits	Range	Language
B0B01LAG	Z,ZK	8	4P+2S	Czech

Relations:

It is not possible to register for the course B0B01LAG if the student is concurrently registered for or has already completed the course B0B01LAGA (mutually exclusive courses).

During a review of study plans, the course B0B01LAGA can be substituted for the course B0B01LAG.

It is not possible to register for the course B0B01LAG 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 B0B01LAG if the student is concurrently registered for or has previously completed the course B0B01LAGA (mutually exclusive courses).

Course guarantor:

Jiří Velebil

Lecturer:

Jiří Velebil

Tutor:

Matěj Dostál, Daria Dunina, Josef Dvořák, Daniel Gromada, Dominik Krasula, Jakub Rondoš, Jiří Velebil, Natalie Žukovec

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. 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.

[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 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	roomT2:C2-85 Dostál M. 11:00–12:30 (lecture parallel2 parallel nr.210) Dejvice CvičebnaroomT2:C4-363 Krasula D. 16:15–17:45 (lecture parallel2 parallel nr.206) Dejvice Cvicebna roomT2:C4-155 Dunina D. 11:00–12:30 (lecture parallel2 parallel nr.211) Dejvice CvičebnaroomT2:C3-54 Krasula D. 14:30–16:00 (lecture parallel2 parallel nr.207) Dejvice T2:C3-54 roomT2:C4-365 Dostál M. 12:45–14:15 (lecture parallel2 parallel nr.208) Dejvice CvičebnaroomT2:C2-82 Velebil J. 14:30–16:00 (lecture parallel2 parallel nr.213) Dejvice T2:C2-82 roomT2:C4-364 Dunina D. 12:45–14:15 (lecture parallel2 parallel nr.212) Dejvice CvicebnaroomT2:C4-365 Dostál M. 14:30–16:00 (lecture parallel2 parallel nr.218) Dejvice Cvičebna
Tue	roomT2:C2-85 14:30–16:00 (lecture parallel2 parallel nr.219) Dejvice Cvičebna
Wed	roomT2:C2-86 Dvořák J. 09:15–10:45 (lecture parallel2 parallel nr.203) Dejvice CvičebnaroomT2:C2-86 Dostál M. 11:00–12:30 (lecture parallel2 parallel nr.202) Dejvice CvičebnaroomT2:C4-78 Žukovec N. 16:15–17:45 (lecture parallel2 parallel nr.215) Dejvice T2:C4-78 roomT2:C4-78 Velebil J. 11:00–12:30 (lecture parallel2 parallel nr.214) Dejvice T2:C4-78roomT2:C4-78 Žukovec N. 12:45–14:15 (lecture parallel2 parallel nr.216) Dejvice T2:C4-78roomT4:D2-256 Velebil J. 14:30–16:00 (lecture parallel2) Dejvice Posluchárna 256 roomT2:C2-86 Dostál M. 12:45–14:15 (lecture parallel2 parallel nr.217) Dejvice Cvičebna
Thu	roomT2:C2-83 Rondoš J. 09:15–10:45 (lecture parallel2 parallel nr.205) Dejvice cvičebnaroomT2:C4-365 Rondoš J. 11:00–12:30 (lecture parallel2 parallel nr.204) Dejvice Cvičebna roomT2:C2-86 11:00–12:30 (lecture parallel2 parallel nr.209) Dejvice Cvičebna
Fri	roomT4:D2-256 Velebil J. 12:45–14:15 (lecture parallel2) Dejvice Posluchárna 256

Time-table for summer semester 2024/2025:

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)