 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Linear Algebra

Code Completion Credits Range Language
BE5B01LAL Z,ZK 8 4P+2S
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:

http://math.feld.cvut.cz/vivi/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.

http://math.feld.cvut.cz/vivi/

Note:
Further information:
http://math.feld.cvut.cz/vivi/
Time-table for winter semester 2019/2020:
 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 roomT2:C2-82Vivi P.11:00–12:30(lecture parallel1)DejvicePosluchárna roomT2:C3-52Vivi P.09:15–10:45(lecture parallel1)DejvicePosluchárnaroomT2:C3-52Vivi P.11:00–12:30(lecture parallel1parallel nr.101)DejvicePosluchárna
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-01-20
For updated information see http://bilakniha.cvut.cz/en/predmet4355406.html