#
MU:MU20006 Algebra II - Course Information

## MU20006 Algebra II

**Mathematical Institute in Opava**

Summer 2022

**Extent and Intensity**- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- doc. RNDr. Zdeněk Kočan, Ph.D. (lecturer)

Mgr. Jan Tesarčík, Ph.D. (seminar tutor) **Guaranteed by**- doc. RNDr. Zdeněk Kočan, Ph.D.

Mathematical Institute in Opava **Prerequisites**(in Czech)-
**MU20005**Algebra I && TYP_STUDIA ( B ) **Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- Mathematical Methods and Modelling (programme MU, Bc-M)
- Mathematical Methods in Economics (programme MU, Bc-M)
- Mathematical Methods in Risk Management (programme MU, Bc-M)
- General Mathematics (programme MU, Bc-M)

**Course objectives**- A student knows basic notions, assertions and algorithms and can use them for solutions of problems in Algebra.
**Syllabus**- - Homomorphisms

- Linear maps (kernel and range, isomorphism)

- Matrix representation of linear maps

- Scalar product (Gramm-Schmidt orthogonalization, orthogonal complement, the norm induced by a scalar product)

- Bilinear and quadratic forms (canonical forms, Sylvester's law of inertia)

- Polynomials

- Eigenvalues and eigenvectors

- First and second decomposition, Jordan basis, Jordan normal form of a matrix

- Tensors (operations on tensors, bases in spaces of tensors, symmetric and antisymmetric tensors, outer product)

- - Homomorphisms
**Literature****Language of instruction**- Czech
**Further comments (probably available only in Czech)**- The course can also be completed outside the examination period.
**Teacher's information**- To get the course-credit, either to satisfactorily consult specified topics or to obtain at least 70 % of points from the written tests.

To pass the exam, to prove at least basic knowledge of the taken subject on the written and the oral parts of the examination.

- Enrolment Statistics (Summer 2022, recent)
- Permalink: https://is.slu.cz/course/sumu/summer2022/MU20006