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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2021/2022

Linear Algebra

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Code Completion Credits Range Language
B0B01LAG Z,ZK 8 4P+2S Czech
The course cannot be taken simultaneously with:
Linear Algebra (A8B01LAG)
Linear Algebra (B0B01LAGA)
The course is a substitute for:
Linear Algebra (B0B01LAGA)
Lecturer:
Jiří Velebil (guarantor)
Tutor:
Jiří Velebil (guarantor), Dominik Beck, Matěj Dostál, Daria Dunina, Josef Dvořák, Daniel Gromada, Karel Pospíšil, Paola Vivi, Jana Vráblíková
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. Intro, polynomials.

2. Linear spaces, linear dependence and independence.

3. Basis, dimensions, coordinates w.r.t. a basis.

4. Matrices, algebra of matrices, determinants. Inverse of a matrix.

5. Systems of linear equations.

6. The description of solutions of homogeneous and inhomogeneous systems of linear equations.

7. Linear mappings. The matrix of a linear mapping.

8. The scalar and the vector product.

9. Applications of scalar product and vector product.

10. The Gram-Schmidt orthogonalisation, orthogonal projections.

11. Eigen vectors and eigenvalues of matrices and linear mappings.

12. Similarity of matrices, diagonalisation, (an outline of) Jordan form.

13. SVD and Moore-Penrose pseudoinverse.

14. Reserve 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 2021/2022:
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:A4-203a
Dvořák J.
11:00–12:30
(lecture parallel2
parallel nr.210)

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

Dejvice
T2:C2-82
roomT2:C4-78
Vráblíková J.
11:00–12:30
(lecture parallel2
parallel nr.211)

Dejvice
T2:C4-78
roomT2:C4-363
Dvořák J.
16:15–17:45
(lecture parallel2
parallel nr.206)

Dejvice
Cvicebna
roomT2:A4-202b

12:45–14:15
(lecture parallel2
parallel nr.208)

Dejvice
Učebna
roomT2:C3-54
Dvořák J.
14:30–16:00
(lecture parallel2
parallel nr.207)

Dejvice
T2:C3-54
roomT2:C2-82
Vráblíková J.
12:45–14:15
(lecture parallel2
parallel nr.212)

Dejvice
T2:C2-82
roomT2:C2-82
Beck D.
14:30–16:00
(lecture parallel2
parallel nr.213)

Dejvice
T2:C2-82
Tue
Wed
roomT2:A4-203b
Dostál M.
09:15–10:45
(lecture parallel2
parallel nr.203)

Dejvice
Učebna
roomT2:A4-203b
Dostál M.
11:00–12:30
(lecture parallel2
parallel nr.202)

Dejvice
Učebna
roomT2:A4-203b
Dostál M.
12:45–14:15
(lecture parallel2
parallel nr.217)

Dejvice
Učebna
roomT2:C4-78

18:00–19:30
(lecture parallel2
parallel nr.219)

Dejvice
T2:C4-78
roomT2:C4-78

11:00–12:30
(lecture parallel2
parallel nr.218)

Dejvice
T2:C4-78
roomT2:D2-256
Velebil J.
14:30–16:00
(lecture parallel2)
Dejvice
T2:D2-256
Thu
roomT2:A4-202a
Dunina D.
09:15–10:45
(lecture parallel2
parallel nr.205)

Dejvice
Ucebna
roomT2:A4-202b
Dunina D.
11:00–12:30
(lecture parallel2
parallel nr.204)

Dejvice
Učebna
roomKN:E-128
Gromada D.
12:45–14:15
(lecture parallel2
parallel nr.215)

Karlovo nám.
Cvičebna K3
roomKN:E-128
Gromada D.
14:30–16:00
(lecture parallel2
parallel nr.216)

Karlovo nám.
Cvičebna K3
roomKN:E-128
Gromada D.
11:00–12:30
(lecture parallel2
parallel nr.214)

Karlovo nám.
Cvičebna K3
Fri
roomT2:D2-256
Velebil J.
12:45–14:15
(lecture parallel2)
Dejvice
T2:D2-256
Time-table for summer semester 2021/2022:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2022-08-15
For updated information see http://bilakniha.cvut.cz/en/predmet4680606.html