MU01806 Algebra II - Exercises

Mathematical Institute in Opava
Summer 2021
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
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.
The course is also listed under the following terms Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2020, Summer 2022.
  • Enrolment Statistics (Summer 2021, recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2021/MU01806