Linear Algebra

Here you can find some basic information about the subject. Pay attention to remarks below, you might find them useful.

• Description
• Credit
• Homework
• Seminary
• Materials

Description

The main aim is to supply working knowledge of basic concepts of linear algebra including their geometric and computational meaning, in order to enable to use these concepts in solution of basic problems of linear algebra. Student should also learn how to use the basic tools of linear algebra in applications.

Credit

You can achieve up to 30 points:

• 4 short tests - 4x6pts
• Homework - 6pts

To gain credit you need to achieve at least 10pts from the tests. In case of 6-9pts there is a possibility to write summary test to achieve necessary points. Homework is sort of voluntary, but I highly recommend to work it up, for it provides easily availible points.

Exam:

A few sample exams (czech)

Homework

To be added.

Seminary

Brief summary of subject matter (PDF, czech)

Seminary programme

1. Complex numbers, basic operations, Gauss plane

2. Elementary matrix and vector calculus

3. Systems of linear equations, Elimination methods

4. FIRST TEST , Inverse matrix, transformation matrices

5. Vector spaces and subspaces

6. Linear dependence and linear combinations

7. SECOND TEST, basis, coordinates, linear mappings

8. Matrix of linear map, nullspace, kernel, billinear forms

9. Quadratic forms and their matrices

10. THIRD TEST, quadratic forms classification, congruences

11. Determinant - calculation, properties, Cramer's rule

12. Eigenvalues and eigenvectors

13. FOURTH TEST, inner product, norm, orthogonality

14. Spare seminary, exam consultations

Materials

Linear Algebra module at mi21 project pages

Šindel, L.: Sbírka řešených příkladů z lineární algebry (PDF, czech)

Strang, G.: Linear algebra and its applications (PDF)

Pages of subject's guarantor, doc. Ing. Petr Beremlijski, Ph.D.