M3130 Linear Algebra and Geometry III

Faculty of Science
Autumn 2008
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)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 15:00–16:50 M1,01017
  • Timetable of Seminar Groups:
M3130/01: Thu 16:00–17:50 M1,01017, M. Čadek
Prerequisites
M2110 Linear Algebra II
Knowledge of basic notions of linear algebra including eigenvalues and eigenvectors, knowledge of quadratic and bilinear forms.
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 and geometry is devoted to the following three topics: quadrics and their classification, multilinear algebra and connection between polynomial matrices and the Jordan canonical form. These topics find applications in differential geometry and ordinary differential equations. At the end of this course, students should be able to understand connections between bilinear forms and the geometry of quadrics, to know basics of multilinear algebra and to compute the Jordan canonical form of a matrix via characteristic matrix.
Syllabus
  • Afinne and projective spaces: definitions, subspaces, endomorphisms, complexification. Quadrics in affine and projective spaces: definitions, projective classification, conjugate points, tangent planes, affine classification. Metric properties of quadrics: main directions, main planes, metric classification. Multilinear algebra: dual space, tensor product, external and symmetric products,coordinates of tensors, functor Hom a its relation to tensor product. Polynomial matrices: equivalence, kanonical forms, connection with characteristic and minimal polynomial, Jordanovým canonical form.
Literature
  • Čadek M: Lineární algebra a geometrie III, elektronický učební text PřF MU Brno, www.math.muni.cz/~cadek
  • Slovák J.: Lineární algebra, elektronický učební text PřF MU Brno, www.math.muni.cz/~slovak
  • Kostrikin A., Manin Yu.: Linear algebra and geometry, Gordon and Breach Science Publishers, 1997
Assessment methods
Form: lectures and exercises. Exam: written and oral Requirements: to know basic theory from the lectures, to obtain internal credit from exarcises.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
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 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, 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 2008, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2008/M3130