MU:MU01806 Algebra II - Exercises - Course Information

MU01806 Algebra II - Exercises

Extent and Intensity

0/2/0. 2 credit(s). Type of Completion: z (credit).

Teacher(s)

Jan Tesarčík (seminar tutor)

Guaranteed by

doc. RNDr. Zdeněk Kočan, Ph.D.
Mathematical Institute in Opava

Timetable of Seminar Groups

MU01806/01: Thu 8:05–9:40 R1, J. Tesarčík

Prerequisites (in Czech)

! MU01906 Algebra II - Exercises && ! MU10832 Algebra II - Exercises && ! MU10932 Algebra II - Exercises && !NOWANY(! MU01906 Algebra II - Exercises , MU10832 Algebra II - Exercises , MU10932 Algebra II - Exercises )

Course Enrolment Limitations

The course is only offered to the students of the study fields 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)

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)

Study Materials
The course can also be completed outside the examination period.

• Enrolment Statistics (Summer 2021, recent)
  
• Permalink: https://is.slu.cz/course/sumu/summer2021/MU01806