Subject description - B0B01LAG

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B0B01LAG Linear Algebra
Roles:P Extent of teaching:4P+2S
Department:13101 Language of teaching:CS
Guarantors:Velebil J. Completion:Z,ZK
Lecturers:Velebil J. Credits:8
Tutors:Too many persons Semester:Z

Web page:


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.

Course outlines:

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.

Exercises outline:


[1] Halmos, P.: Finite-dimensional vector spaces,2nd edition, Springer 2000.
[2] Strang, G.: Introduction to linear algebra, 5th edition, Wellesley-Cambridge 2016.


Subject is included into these academic programs:

Program Branch Role Recommended semester
BPKYR_2016 Common courses P 1
BPOI_BO_2018 Common courses P 1
BPOI4_2018 Computer Games and Graphics P 1
BPOI3_2018 Software P 1
BPOI2_2018 Internet of Things P 1
BPOI1_2018 Artificial Intelligence and Computer Science P 1
BPOI1_2016 Computer and Information Science P 1
BPOI_BO_2016 Common courses P 1
BPOI4_2016 Computer Games and Graphics P 1
BPOI3_2016 Software P 1
BPOI2_2016 Internet of Things P 1
BPEK_2016 Common courses P 1
BPKYR_2021 Common courses P 1
BPEEM1_2016 Applied Electrical Engineering P 1
BPEEM_BO_2016 Common courses P 1
BPEEM2_2016 Electrical Engineering and Management P 1

Page updated 21.5.2024 17:51:15, semester: Z/2024-5, Z,L/2023-4, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)