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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2021/2022

Linear Algebra

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Code Completion Credits Range Language
BE5B01LAL Z,ZK 8 4P+2S English
Lecturer:
Paola Vivi (guarantor)
Tutor:
Paola Vivi (guarantor)
Supervisor:
Department of Mathematics
Synopsis:

The course covers standard basics of matrix calculus (determinants, inverse matrix) and linear algebra (basis, dimension, inner product spaces, linear transformations) including eigenvalues and eigenvectors. Matrix similarity, orthogonal bases, and bilinear and quadratic forms are also covered.

Requirements:

https://math.fel.cvut.cz/en/people/vivipaol/LAL2015.pdf

Syllabus of lectures:

1. Polynomials. Introduction to systems of linear equations and Gauss elimination method.

2. Linear spaces, linear dependence and independence.

3. Basis, dimension, coordinates of vectors.

4. Matrices: operations, rank, transpose.

5. Determinant and inverse of a matrix.

6. Structure of solutions of systems of linear equations. Frobenius Theorem.

7. Linear mappings. Matrix of a linear mapping.

8. Free vectors. Dot product and cross product.

9. Lines and planes in 3-dimensional real space.

10. Eigenvalues and eigenvectors of matrices and linear mappings.

11. Similarity of matrices, matrices similar to diagonal matrices.

12. Euclidean space, orthogonalization, orthonormal basis. Fourier basis.

13. Introduction to bilinear and quadratic forms.

Syllabus of tutorials:

1. Polynomials. Introduction to systems of linear equations and Gauss elimination method.

2. Linear spaces, linear dependence and independence.

3. Basis, dimension, coordinates of vectors.

4. Matrices: operations, rank, transpose.

5. Determinant and inverse of a matrix.

6. Structure of solutions of systems of linear equations. Frobenius Theorem.

7. Linear mappings. Matrix of a linear mapping.

8. Free vectors. Dot product and cross product.

9. Lines and planes in 3-dimensional real space.

10. Eigenvalues and eigenvectors of matrices and linear mappings.

11. Similarity of matrices, matrices similar to diagonal matrices.

12. Euclidean space, orthogonalization, orthonormal basis. Fourier basis.

13. Introduction to bilinear and quadratic forms.

Study Objective:
Study materials:

1. P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 2005.

2. P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 1997.

https://math.fel.cvut.cz/en/people/vivipaol/LAL2015.pdf

Note:
Further information:
https://math.fel.cvut.cz/en/people/vivipaol/BE5B01LAL.html
Time-table for winter semester 2021/2022:
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
roomT2:C2-82
Vivi P.
11:00–12:30
(lecture parallel1)
Dejvice
T2:C2-82
Wed
Thu
roomT2:C3-52
Vivi P.
09:15–10:45
(lecture parallel1)
Dejvice
T2:C3-52
roomT2:C3-52
Vivi P.
11:00–12:30
(lecture parallel1
parallel nr.101)

Dejvice
T2:C3-52
Fri
Time-table for summer semester 2021/2022:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2022-08-13
For updated information see http://bilakniha.cvut.cz/en/predmet4355406.html