Linear Algebra

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

This course covers introductory topics of linear algebra. The main focus

is on

the related notions of linear spaces and linear transformations (linear

independence, bases and coordinates) and matrices (determinants, inverse

matrix, matrix of a linear mapping, eigenvalues). Applications include

solving systems of linear equations, geometry in 3-space (including dot

product and cross product), and solving linear differential equations.

Requirements:

Syllabus of lectures:

1. Introduction, polynomials.

2. Linear spaces, linear dependence and independence.

3. Basis, dimension, coordinates of vectors.

4. Matrices, operations, determinants. Inverse matrix.

5. Systems of linear equations.

6. Linear mappings. Matrix of a linear mapping.

7. Free vectors. Dot product and cross product.

8. Lines and planes in 3-dimensional Euclidean space.

9. Eigenvalues and eigenvectors of matrices and linear mappings.

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

11. Generalized eigenvectors.

12. Systems of linear differential equations of 1st order with constant coefficients.

13. Linear differential equations of order n with constant coefficients.

14. Back-up class.

Syllabus of tutorials:

1. Polynomials.

2. Examples of linear spaces, linear independence.

3. Basis, coordinates of vectors.

4. Operations with matrices, determinants. Finding inverse matrix.

5. Systems of linear equations.

6. Examples of linear mappings.

7. Matrix of a linear mapping, change of basis.

8. Dot product and cross product in geometry. Lines and planes.

9. Eigenvalues and eigenvectors of matrices.

10. Diagonalization of matrices.

11. Generalized eigenvectors and applications.

12. Systems of linear differential equations.

13. Linear differential equations of order n.

14. Back-up class.

Study Objective:

Study materials:

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

Note:

Further information:

http://math.feld.cvut.cz/0educ/pozad/a0b01lag.htm

No time-table has been prepared for this course

The course is a part of the following study plans:

• Elektrotechnika, energetika a management - Aplikovaná elektrotechnika_162957 (elective course)
• Elektrotechnika, energetika a management - Elektrotechnika a management_163134 (elective course)
• Kybernetika a robotika - Robotika_163230 (compulsory course in the program)
• Kybernetika a robotika - Senzory a přístrojová technika_163253 (compulsory course in the program)
• Kybernetika a robotika - Systémy a řízení_163315 (compulsory course in the program)
• Komunikace, multimédia a elektronika - Komunikační technika_163439 (elective course)
• Komunikace, multimédia a elektronika - Multimediální technika_163458 (elective course)
• Komunikace, multimédia a elektronika - Aplikovaná elektronika_163524 (elective course)
• Komunikace, multimédia a elektronika - Síťové a informační technologie_163540 (elective course)
• Otevřená informatika - Počítačové systémy (compulsory course in the program)
• Otevřená informatika - Informatika a počítačové vědy (compulsory course in the program)
• Otevřená informatika - Softwarové systémy (compulsory course in the program)
• Elektrotechnika, energetika a management, před rozřazením do oborů (elective course)
• Komunikace, multimédia a elektronika, před rozřazením do oborů (elective course)
• Kybernetika a robotika, před rozřazením do oborů (compulsory course in the program)
• Otevřená informatika, před rozřazením do oborů (compulsory course in the program)
• Inteligentní systémy (STM-A7B-přechodné) (elective course)
• Manažerská informatika (STM-A7B-přechodné) (elective course)
• Web a multimedia (STM-A7B-přechodné) (elective course)
• Softwarové inženýrství (STM-A7B-přechodné) (elective course)
• Společný 1.ročník (STM-A7B) (elective course)
• Inteligentní systémy (STM-A7B) (elective course)
• Manažerská informatika (STM-A7B) (elective course)
• Softwarové inženýrství (STM-A7B) (elective course)
• Web a multimedia (STM-A7B) (elective course)