Course: Algebra II

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Course title Algebra II
Course code MU/10006
Organizational form of instruction Lecture
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • KOČAN Zdeněk, doc. RNDr. Ph.D.
Course content
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)

Learning activities and teaching methods
Recommended literature
  • J. Musilová, D. Krupka. Lineární a multilineární algebra. Univerzita J. E. Purkyně v Brně, Brno, 1989.
  • J. T. Moore. Elements of Linear Algebra and Matrix Theory. McGraw Hill, New York, 1968.
  • M. Marvan. Algebra II. MÚ SU,, Opava, 1999.
  • M. Marvan. Algebra I. MÚ SU, Opava, 1999.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Applied Mathematics in Risk Management (3) Mathematics courses 1 Summer
Mathematical Institute in Opava Mathematical Methods in Economics (3) Economy 1 Summer