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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

Linear Algebra

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Code Completion Credits Range Language
B0B01LAG Z,ZK 8 4P+2S Czech
Vztahy:
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).
Garant předmětu:
Jiří Velebil
Lecturer:
Jiří Velebil
Tutor:
Matěj Dostál, Daria Dunina, Josef Dvořák, Daniel Gromada, Dominik Krasula, Karel Pospíšil, 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 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
roomT2:C2-85
Dvořák J.
11:00–12:30
(lecture parallel2
parallel nr.210)

Dejvice
Cvičebna
roomT2:C2-82
Krasula D.
16:15–17:45
(lecture parallel2
parallel nr.201)

Dejvice
T2:C2-82
roomT2:C4-155
Dunina D.
11:00–12:30
(lecture parallel2
parallel nr.211)

Dejvice
Cvičebna
roomT2:C4-363
Dvořák J.
16:15–17:45
(lecture parallel2
parallel nr.206)

Dejvice
Cvicebna
roomT2:C4-365
Pospíšil K.
12:45–14:15
(lecture parallel2
parallel nr.208)

Dejvice
Cvičebna
roomT2:C3-54
Pospíšil K.
14:30–16:00
(lecture parallel2
parallel nr.207)

Dejvice
T2:C3-54
roomT2:C4-364
Dunina D.
12:45–14:15
(lecture parallel2
parallel nr.212)

Dejvice
Cvicebna
roomT2:C2-82
Krasula D.
14:30–16:00
(lecture parallel2
parallel nr.213)

Dejvice
T2:C2-82
roomT2:C3-52
Dvořák J.
14:30–16:00
(lecture parallel2
parallel nr.218)

Dejvice
T2:C3-52
Tue
roomT2:C2-85
Pospíšil K.
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
Cvičebna
roomT2:C2-86
Dvořák J.
11:00–12:30
(lecture parallel2
parallel nr.202)

Dejvice
Cvičebna
roomT2:C4-78
Žukovec N.
16:15–17:45
(lecture parallel2
parallel nr.215)

Dejvice
T2:C4-78
roomT2:C4-78
Pospíšil K.
11:00–12:30
(lecture parallel2
parallel nr.214)

Dejvice
T2:C4-78
roomT2:C4-78
Žukovec N.
12:45–14:15
(lecture parallel2
parallel nr.216)

Dejvice
T2:C4-78
roomT4:D2-256
Velebil J.
14:30–16:00
(lecture parallel2)
Dejvice
Posluchárna 256
roomT2:C2-86
Dvořák J.
12:45–14:15
(lecture parallel2
parallel nr.217)

Dejvice
Cvičebna
Thu
roomT2:C2-83
Dvořák J.
09:15–10:45
(lecture parallel2
parallel nr.205)

Dejvice
cvičebna
roomT2:C4-365
Dvořák J.
11:00–12:30
(lecture parallel2
parallel nr.204)

Dejvice
Cvičebna
Fri
roomT4:D2-256
Velebil J.
12:45–14:15
(lecture parallel2)
Dejvice
Posluchárna 256
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-07-16
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet4680606.html