PřF:M3130 Linear Algebra III - Course Information
M3130 Linear Algebra and Geometry III
Faculty of ScienceAutumn 2011
- Extent and Intensity
- 2/2. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. Lukáš Vokřínek, PhD. (lecturer)
- Guaranteed by
- doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Tue 12:00–13:50 M1,01017
- Timetable of Seminar Groups:
M3130/02: Wed 16:00–17:50 M5,01013, L. Vokřínek - 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
- Mathematics (programme PřF, M-MA)
- 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 linear differential equations.
At the end of this course students should be able to:
*understand the connection between bilinear forms and the geometry of quadrics
*derive geometric properties of quadrics
*compute with tensors both in coordinates and without them
*utilize a different method of finding the Jordan canonical form of a matrix - Syllabus
- Affine and projective spaces: definitions, subspaces, homomorphisms, projective closure, complexification.
- Quadrics in affine and projective spaces: definitions, projective classification, conjugate points, tangent planes.
- Metric properties of quadrics: principal directions, principal planes, metric classification.
- Selected applications: spectral decomposition, Moore-Penrose pseudoinverse, Markov chains
- Multilinear algebra: dual space, tensor product, exterior and symmetric products, tensor coordinates, functor Hom and its relation to the tensor product.
- Integer matrices: equivalence, Smith normal form, classification of finitely generated commutative groups
- Polynomial matrices: equivalence, Smith normal form, connection with characteristic and minimal polynomial, Jordan 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
- LANG, Serge. Linear Algebra. Third Edition. New York: Springer-Verlag, 1987, 296 pp. ISBN 0-387-96412-6. info
- Teaching methods
- Lectures and tutorials.
- Assessment methods
- Over the semester there will be two written tests at the tutorials. It is required to obtain in total at least half of the points.
The exam consists of a written and an oral part. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually. - Teacher's information
- http://www.math.muni.cz/~cadek
- Enrolment Statistics (Autumn 2011, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2011/M3130