MU:MU01906 Algebra II - Exercises

MU01906 Algebra II - Exercises

Mathematical Institute in Opava
Summer 2014

Extent and Intensity

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

Teacher(s)

Guaranteed by

RNDr. Oldřich Stolín, Ph.D.
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. Linear maps (kernel and range, linear isomorphism, matrix representation)
2. Structure of linear operators (eigenvalues and eigenvectors, first and second decomposition, Jordan basis, Jordan normal form of a matrix)
3. Scalar product (Gramm-Schmidt orthogonalization, orthogonal complement, the norm induced by a scalar product)
4. Bilinear and quadratic forms (canonical forms, Sylvester's law of inertia)
5. 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.