CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

Linear Algebra

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 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 roomT2:C2-8511:00–12:30(lecture parallel2parallel nr.210)DejviceCvičebnaroomT2:C2-8216:15–17:45(lecture parallel2parallel nr.201)DejviceT2:C2-82 roomT2:C4-15511:00–12:30(lecture parallel2parallel nr.211)DejviceCvičebnaroomT2:C4-36316:15–17:45(lecture parallel2parallel nr.206)DejviceCvicebna roomT2:C4-36512:45–14:15(lecture parallel2parallel nr.208)DejviceCvičebnaroomT2:C3-5414:30–16:00(lecture parallel2parallel nr.207)DejviceT2:C3-54 roomT2:C4-36412:45–14:15(lecture parallel2parallel nr.212)DejviceCvicebnaroomT2:C2-8214:30–16:00(lecture parallel2parallel nr.213)DejviceT2:C2-82 roomT2:C3-5214:30–16:00(lecture parallel2parallel nr.218)DejviceT2:C3-52 roomT2:C2-8514:30–16:00(lecture parallel2parallel nr.219)DejviceCvičebna roomT2:C2-8609:15–10:45(lecture parallel2parallel nr.203)DejviceCvičebnaroomT2:C2-8611:00–12:30(lecture parallel2parallel nr.202)DejviceCvičebnaroomT2:C4-78Žukovec N.16:15–17:45(lecture parallel2parallel nr.215)DejviceT2:C4-78 roomT2:C4-7811:00–12:30(lecture parallel2parallel nr.214)DejviceT2:C4-78roomT2:C4-78Žukovec N.12:45–14:15(lecture parallel2parallel nr.216)DejviceT2:C4-78roomT4:D2-256Velebil J.14:30–16:00(lecture parallel2)DejvicePosluchárna 256 roomT2:C2-8612:45–14:15(lecture parallel2parallel nr.217)DejviceCvičebna roomT2:C2-8309:15–10:45(lecture parallel2parallel nr.205)DejvicecvičebnaroomT2:C4-36511:00–12:30(lecture parallel2parallel nr.204)DejviceCvičebna roomT4:D2-256Velebil J.12:45–14:15(lecture parallel2)DejvicePosluchárna 256
Time-table for summer semester 2024/2025:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-06-16
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet4680606.html