MU:MU20006 Algebra II - Course Information
MU20006 Algebra IIMathematical Institute in Opava
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- 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
- 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.
- - 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)
- 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)
- - Homomorphisms
- required literature
- M. Marvan. Algebra I. MÚ SU, Opava, 1999. URL info
- M. Marvan. Algebra II. MÚ SU,, Opava, 1999. URL info
- Language of instruction
- Further comments (probably available only in Czech)
- 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.