MU01906 Algebra II - Exercises

Mathematical Institute in Opava
Summer 2015
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. Michal Marvan, CSc.
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
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)
The course can also be completed outside the examination period.
The course is also listed under the following terms Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2020, Summer 2021.
  • Enrolment Statistics (Summer 2015, recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2015/MU01906