MU01016 Algebra II

Mathematical Institute in Opava
Summer 2015
Extent and Intensity
2/0/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Marvan, CSc. (lecturer)
Guaranteed by
doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
( MU01015 Algebra I || MU10005 Algebra I ) && ( MU01806 Algebra II - Exercises || MU01906 Algebra II - Exercises )
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 which takes up the course Algebra I, students get basic knowledge about linear algebra necessary for the further study of mathematics.
Syllabus
  • 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)
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.
Teacher's information
Before the exam all students have to meet the requirements for the credit of Algebra II-Exercises in the current academic year. For a successful graduation it is necessary to prove at least basic knowledge of the taken subject on the written and the oral parts of the examination.
The course is also listed under the following terms Winter 1998, Summer 1999, Winter 1999, Summer 2000, Winter 2000, Summer 2001, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2020, Summer 2021.
  • Enrolment Statistics (Summer 2015, recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2015/MU01016