Lecturer(s)


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 (GrammSchmidt 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

unspecified

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.
