MU:MU01806 Algebra II - Exercises - Course Information
MU01806 Algebra II - Exercises
Mathematical Institute in OpavaSummer 2019
- Extent and Intensity
- 0/2/0. 2 credit(s). Type of Completion: z (credit).
- Teacher(s)
- Mgr. Zuzana Roth, Ph.D. (seminar tutor)
- Guaranteed by
- doc. RNDr. Zdeněk Kočan, Ph.D.
Mathematical Institute in Opava - 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
- Astrophysics (programme FPF, B1701 Fyz)
- Course objectives
- In the course the students will be practising and extending of their knowledges obtained in the course Algebra II.
- 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
- recommended 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
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
- Enrolment Statistics (Summer 2019, recent)
- Permalink: https://is.slu.cz/course/sumu/summer2019/MU01806