CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2020/2021

# Linear Algebra B 2

Code Completion Credits Range Language
818LI2 Z,ZK 4 1+2 Czech
Lecturer:
Dana Majerová (guarantor)
Tutor:
Dana Majerová (guarantor)
Supervisor:
Department of Software Engineering
Synopsis:

Determinant. Regular matrix, regular operator. Inverse matrix and operator. Inner product, orthogonality, Gramm-Schmidt orthogonalization process. Linear geometry. Eigenvalues, eigenvectors, diagonalization of matrices. Special types of matrices.

Requirements:
Syllabus of lectures:

1. permutation

2. determinant definition, basic properties

3. cofactor expansion along the row or column

4. use of determinants, Cramer's rule

5. inner product, orthogonal base, Gramm-Schmidt orthogonalization process

6. orthonormal matrix

7. orthogonal complement

8. affine varieties (basic terms)

9. position of affine varieties

10. distance of affine varieties

11. eigenvalue and eigenvector (basic terms)

12. matrix similarity

13. symetric and orthonormal matrices

Syllabus of tutorials:

1. permutation

2. determinant definition, basic properties

3. cofactor expansion along the row or column

4. use of determinants, Cramer's rule

5. inner product, orthogonal base, Gramm-Schmidt orthogonalization process

6. orthonormal matrix

7. orthogonal complement

8. affine varieties (basic terms)

9. position of affine varieties

10. distance of affine varieties

11. eigenvalue and eigenvector (basic terms)

12. matrix similarity

13. symetric and orthonormal matrices

Study Objective:

Knowledge of basic terms of linear algebra.

Ability to prove mathematical theorems and solve problems of linear algebra, especially work with matrices.

Study materials:

Key references:

[1] Dontová, E. Matematika III. Praha: ČVUT, 1999.

[2] Čížková, L. Sbírka příkladů z matematiky I. Praha: ČVUT, 1999.