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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2022/2023

Linear Algebra 2

The course is not on the list Without time-table
Code Completion Credits Range Language
BIE-LA2.21 Z,ZK 5 2P+2C English
Lecturer:
Karel Klouda (guarantor), Marzieh Forough
Tutor:
Karel Klouda (guarantor), Marzieh Forough
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
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2022-10-05
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet6579406.html