# MU:MU01016 Algebra II - Course Information

## MU01016 Algebra II

**Mathematical Institute in Opava**

Summer 2016

**Extent and Intensity**- 2/0/0. 4 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- doc. RNDr. Zdeněk Kočan, Ph.D. (lecturer)
**Guaranteed by**- doc. RNDr. Zdeněk Kočan, Ph.D.

Mathematical Institute in Opava **Prerequisites**(in Czech)- (
**MU01015**Algebra I ||**MU10005**Algebra I ) && (**MU01806**Algebra II - Exercises ||**MU01906**Algebra II - Exercises ) **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**- Applied Mathematics (programme MU, B1101)
- Mathematics (programme MU, B1101)

**Course objectives**- In the course which takes up the course Algebra I, students get basic knowledge about linear algebra necessary for the further study of mathematics.
**Syllabus**- 1. Vector spaces, vector subspaces

2. Linear maps (kernel and range, linear isomorphism, matrix representation)

3. Structure of linear operators (eigenvalues and eigenvectors, first and second decomposition, Jordan basis, Jordan normal form of a matrix)

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

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

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

- 1. Vector spaces, vector subspaces
**Literature**- M. Marvan.
*Algebra I*. MÚ SU, Opava, 1999. URL info - M. Marvan.
*Algebra II*. MÚ SU,, Opava, 1999. URL info - J. Musilová, D. Krupka.
*Lineární a multilineární algebra*. Univerzita J. E. Purkyně v Brně, Brno, 1989. info - J. T. Moore.
*Elements of Linear Algebra and Matrix Theory*. McGraw Hill, New York, 1968. info

*recommended literature*- M. Marvan.
**Language of instruction**- Czech
**Further comments (probably available only in Czech)**- The course can also be completed outside the examination period.
**Teacher's information**- Before the exam all students have to meet the requirements for the credit of Algebra II-Exercises in the current academic year. For a successful graduation it is necessary to prove at least basic knowledge of the taken subject on the written and the oral parts of the examination.

- Enrolment Statistics (Summer 2016, recent)
- Permalink: https://is.slu.cz/course/sumu/summer2016/MU01016