## MA004 Linear Algebra and Geometry II

Faculty of Informatics
Spring 2005
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Faculty of Informatics
Contact Person: doc. RNDr. Martin Čadek, CSc.
Timetable
Thu 14:00–15:50 U5
Prerequisites
! M004 Linear Algebra and Geometry II
Knowledge of basic notions of linear algebra is supposed.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions such as affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators. In more details the spaces with scalar product and properties of orthogonal and selfadjoint operators are examined. All is applied in affine and Euclidean geometry. At the end we deal with the Jordan canonical form.
Syllabus
• Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal a unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
• Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita,1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
• Zlatoš, Pavol. Lineárna algebra a geometria. Předběžné učební texty MFF UK v Bratislavě.
Assessment methods (in Czech)
Početní a teoretické zvládnutí přednesené látky (porozumnění základním pojmům a větám, jednoduché důkazy).
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information