Universität Wien
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250014 VO Linear algebra and geometry 2 (2015W)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 05.10. 09:45 - 12:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 12.10. 09:45 - 12:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 19.10. 09:45 - 12:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.11. 09:45 - 12:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.11. 09:45 - 12:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.11. 09:45 - 12:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.11. 09:45 - 12:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.12. 09:45 - 12:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.12. 09:45 - 12:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.01. 09:45 - 12:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 18.01. 09:45 - 12:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Normal forms of linear maps: representation by triangular matrices, Cayley-Hamilton theorem, algebra of polynomials, primary decomposition, nilpotent maps, Jordan decomposition and Jordan normal form.
Multilinear algebra: tensor products of vector spaces, universal property, contractions and tensorial operations, symmetric and alternating multilinear maps, symmetric powers and exterior powers, exterior algebra, Clifford algebras (if time permits).

Assessment and permitted materials

written and/or oral exam after the end of the course

Minimum requirements and assessment criteria

The students thoroughly understand some advances aspects of linear algebra and the basics of multilinear algebra. They recognize the role of the algebraic theory of polynomials in the description of linear maps and are able do deal with Jordan normal forms, both in a theoretical and in a practical context. They understand tensors and their relations to multilinear maps, in particular in the case alternating multllinear forms.

Examination topics

lecture course

Reading list

lecture notes will be available online at http://www.mat.univie.ac.at/~cap/lectnotes.html

Association in the course directory

LAG

Last modified: Mo 07.09.2020 15:40