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2024/2025
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Welcome page > Faculty of Information Technology > Department of Applied Mathematics > Linear Algebra 2

Linear Algebra 2

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Code Completion Credits Range Language
BI-LA2.21 Z,ZK 5 2P+2C Czech
Course guarantor:
Karel Klouda
Lecturer:
Luděk Kleprlík, Karel Klouda, Jakub Šístek
Tutor:
Daniel Dombek, Luděk Kleprlík, Karel Klouda, Jan Legerský, Marta Nollová, Jakub Šístek
Supervisor:
Department of Applied Mathematics
Synopsis:

Studenti si v tomto předmětu rozšíří znalosti z předmětu BI-LA1, kde se pracovalo pouze s vektory ve formě n-tic čísel. Zde si zavedeme vektorový prostor v abstraktní obecné formě. Seznámíme se také s pojmem skalární součin a lineární zobrazení, což nám dovolí ukázat souvislost s lineární algebrou, geometrií a počítačovou grafikou. Dalším velkým tématem bude numerická lineární algebra, kde si ukážeme potíže s řešením soustav lineárních rovnic na počítači a možnosti, jak se s tímto problémem vypořádat s důrazem na rozklady matic. Ukážeme si také aplikace lineární algebry v různých oborech.

Requirements:

We assume the students finished course BI-LA1.21.

Syllabus of lectures:

1. Abstract vector spaces, infinite-dimensional vector spaces.

2. Scalar products, vector norm, orthogonality.

3. Scalar products and analytical geometry.

4. [2] Linear maps and their matrices.

6. Affine transformations, homogeneous coordinates, projections and operations in 3D space as linear maps.

7. Introduction to numerical mathematics.

8. Solving systems of linear equations on computers.

9. [2] Matrix factorizations (LU, SVD, QR): computation and applications.

11. [3] Applications of linear algebra: the least-squares method, linear programming, recurrent equations.

Syllabus of tutorials:

1. Abstract vector spaces.

2. Scalar products, vector norm, orthogonality.

3. Analytical geometry.

4. Linear maps.

5. Matrices of linear maps.

6. [2] Affine transformations, homogeneous coordinates, projections and operations in 3D space as linear maps.

8. Systems of linear equations.

9. [2] Matrix factorizations (LU, SVD, QR).

11. The least-squares method.

12. Linear programming.

13. Recurrent equations.

Study Objective:
Study materials:

1. Lloyd N. T., David B. : Numerical Linear Algebra. SIAM, 1997. ISBN 978-0898713619.

2. Lyche T. : Numerical Linear Algebra and Matrix Factorizations. Springer, 2020. ISBN 978-3030364670.

3. Gentle J. E. : Matrix Algebra: Theory, Computations and Applications in Statistics (2nd Edition). Springer, 2017. ISBN 978-3319648668.

4. Lengyel E. : Mathematics for 3D Game Programming and Computer Graphics (3rd Edition). Cengage Learning PTR, 2011. ISBN 978-1435458864.

Note:
Further information:
http://courses.fit.cvut.cz/BI-LA2
Time-table for winter semester 2024/2025:
Time-table is not available yet
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 2024-11-23
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