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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

Linear Algebra 2

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Code Completion Credits Range Language
BIE-LA2.21 Z,ZK 5 2P+2C English
Garant předmětu:
Karel Klouda
Lecturer:
Marzieh Forough, Karel Klouda
Tutor:
Marzieh Forough, Karel Klouda
Supervisor:
Department of Applied Mathematics
Synopsis:

Students will broaden their knowledge gained in the BIE-LA1 introductory course, where only vectors in the form of n-tuples of numbers were considered. Here we will introduce vector spaces in a general abstract form. The notions of a scalar product and a linear map will enable to demonstrate the profound link between linear algebra, geometry, and computer graphics. The other main topic will be numerical linear algebra, in particular problems with solving systems of linear equations on computers. The issues of numerical linear algebra will be demonstrated mainly on the matrix factorization problem. Selected applications of linear algebra in various fields will be presented.

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 2023/2024:
Time-table is not available yet
Time-table for summer 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
Tue
Wed
Thu
roomTH:A-s135
Forough M.
11:00–12:30
(lecture parallel1)
Thákurova 7 (budova FSv)
As135
roomTH:A-942
Forough M.
16:15–17:45
(lecture parallel1
parallel nr.102)

Thákurova 7 (budova FSv)
roomTH:A-942
Forough M.
14:30–16:00
(lecture parallel1
parallel nr.101)

Thákurova 7 (budova FSv)
Fri
The course is a part of the following study plans:
Data valid to 2024-05-25
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