MU20006 Algebra II

Mathematical Institute in Opava
Summer 2021
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Zdeněk Kočan, Ph.D. (lecturer)
Mgr. Jan Tesarčík, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Zdeněk Kočan, Ph.D.
Mathematical Institute in Opava
Timetable
Tue 13:05–14:40 R1
  • Timetable of Seminar Groups:
MU20006/01: Thu 8:05–9:40 R1, J. Tesarčík
Prerequisites (in Czech)
MU20005 Algebra I && TYP_STUDIA ( B )
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
A student knows basic notions, assertions and algorithms and can use them for solutions of problems in Algebra.
Syllabus
  • - Homomorphisms
    - Linear maps (kernel and range, isomorphism)
    - Matrix representation of linear maps
    - Scalar product (Gramm-Schmidt orthogonalization, orthogonal complement, the norm induced by a scalar product)
    - Bilinear and quadratic forms (canonical forms, Sylvester's law of inertia)
    - Polynomials
    - Eigenvalues and eigenvectors
    - First and second decomposition, Jordan basis, Jordan normal form of a matrix
    - Tensors (operations on tensors, bases in spaces of tensors, symmetric and antisymmetric tensors, outer product)
Literature
    required literature
  • M. Marvan. Algebra I. MÚ SU, Opava, 1999. URL info
  • M. Marvan. Algebra II. MÚ SU,, Opava, 1999. URL info
    recommended literature
  • 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.
Teacher's information
To get the course-credit, either to satisfactorily consult specified topics or to obtain at least 70 % of points from the written tests.
To pass the exam, to prove at least basic knowledge of the taken subject on the written and the oral parts of the examination.

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