 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Linear Algebra and its Applications

The course is not on the list Without time-table
Code Completion Credits Range Language
AE0B01LAA Z,ZK 8 3+3
Lecturer:
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

The course covers standard basics of matrix calculus (determinants, inverse matrix) and linear algebra (linear space,basis, dimension, euclidean spaces, linear transformations) including eigenvalues and eigenvectors. Notions are illustrated in applications: matrices are used when solving systems of linear equations, eigenvalues are used for solving systems of linear differential equations.

Requirements:

In order to obtain the certificate of attendance,

students are required to actively participate in the laboratory class, hand in the assigned

homework and obtain a sufficient score during lab tests. Only students who obtain attendance certificate („zapocet“) are allowed to take the exam.

http://math.feld.cvut.cz/vivi/AE0B01LAA2010.pdf

Syllabus of lectures:

1.Systems of linear equations. Gauss elimination method.

2. Linear spaces, linear dependence and independence.

3. Basis, dimension, coordinates of vectors.

4. Rank of a matrix, the Frobenius theorem.

5. Linear mappings. Matrix of a linear mapping.

6. Matrix multiplication, inverse matrix. Determinants.

7.Inner product.Expanding vector w.r.t. orthonormal basis. Fourier basis.

8. Eigenvalues and eigenvectors of matrices and linear mappings.

9. Differential equations. Method of separation of variables.

10. Linear differential equations, homogeneous and non-homogeneous. Variation of parameter.

11.Linear differential equations with constant coefficients. Basis of solutions. Solving

non-homogeneous differential equations.

12.Systems of linear differential equations with constant coefficients. Basis of solutions.Solving non-homogeneous systems.

13.Applications. Numerical aspects.

Syllabus of tutorials:

1.Systems of linear equations. Gauss elimination method.

2. Linear spaces, linear dependence and independence.

3. Basis, dimension, coordinates of vectors.

4. Rank of a matrix, the Frobenius theorem.

5. Linear mappings. Matrix of a linear mapping.

6. Matrix multiplication, inverse matrix. Determinants.

7.Inner product.Expanding vector w.r.t. orthonormal basis. Fourier basis.

8. Eigenvalues and eigenvectors of matrices and linear mappings.

9. Differential equations. Method of separation of variables.

10. Linear differential equations, homogeneous and non-homogeneous. Variation of parameter.

11.Linear differential equations with constant coefficients. Basis of solutions. Solving

non-homogeneous differential equations.

12.Systems of linear differential equations with constant coefficients. Basis of solutions.Solving non-homogeneous systems.

13.Applications. Numerical aspects.

Study Objective:
Study materials:

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

2. P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 1997. ftp://math.feld.cvut.cz/pub/krajnik/vyuka/ua/linalgeb.pdf

Note:
Further information:
http://math.feld.cvut.cz/vivi/
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2020-01-21
For updated information see http://bilakniha.cvut.cz/en/predmet12773104.html