M3130 Linear Algebra and Geometry III

Faculty of Science
Autumn 2002
Extent and Intensity
2/2. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
prof. RNDr. Jan Paseka, CSc. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Čadek, CSc.
Prerequisites
M2110 Linear algebra II
Knowledge of basic notion of linear algebra including eigenvalues and eigenvectors.
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
The third from the series of lectures on linear algebra is devoted to more advanced topics: the structure of linear endomorphisms (including Jordan canonical form) and multilinear algebra. These topics find applications in ordinary differential equations, differential geometry and physics.
Syllabus
  • Geometry of linear endomorphisms: eigenvalues, root subspaces, nilpotent and cyclic endomorphisms, Jordan canonical form. Polynomial matrices: equivalence, canonical form, connection with characteristic and minimal polynomials and with the Jordan canonical form. Duality: dual vector space, dual basis, dual morphism. Multilinear algebra: tensor product, equivalence of different definitions, change of coordinates, functor Hom and its reletion to tensor product.
Literature
  • Kostrikin A., Manin Yu.: Linear algebra and geometry, Gordon and Breach Science Publishers, 1997
  • Slovák J.: Lineární algebra, elektronický učební text PřF MU Brno, www.math.muni.cz/~slovak
Assessment methods (in Czech)
Výuka: přednáška a klasická cvičení. Zkouška: písemná a ústní.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2002, recent)
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