PřF:M3130 Linear Algebra III - Course Information
M3130 Linear Algebra and Geometry III
Faculty of ScienceAutumn 2011 - acreditation
The information about the term Autumn 2011 - acreditation is not made public
- 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. RNDr. Martin Čadek, CSc. (lecturer)
- Guaranteed by
- doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science - 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 offered to students of any study field.
- 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, complexification.
- Quadrics in affine and projective spaces: definitions, projective classification, conjugate points, tangent planes, affine classification.
- Metric properties of quadrics: principal directions, principal planes, metric classification.
- Multilinear algebra: dual space, tensor product, external and symmetric products, coordinates of tensors, functor Hom and its relation to the tensor product.
- Polynomial matrices: equivalence, canonical forms, 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
- 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)
- The course is taught annually.
The course is taught: every week. - Teacher's information
- http://www.math.muni.cz/~cadek
- Enrolment Statistics (Autumn 2011 - acreditation, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2011-acreditation/M3130