Linear Algebra I - NUMP003
Title: Lineární algebra I Department of Mathematics Education (32-KDM) Faculty of Mathematics and Physics from 2016 winter 5 winter s.:2/2, C+Ex [HT] unlimited unlimited no no cancelled Czech full-time full-time
Guarantor: doc. RNDr. Jindřich Bečvář, CSc. Mathematics > AlgebraTeaching > Mathematics NALG001, NALG002, NMAI057, NMAI058 NALG001, NMUE024, NMUM103 NMAF012, NMUM103, NMUM802, NALG003, NMAI045, NMAF031 NMAF031, NMUM802, NMUM103, NMUE024
 Annotation - ---CzechEnglish
Introduction to basic algebraic structures. Vector spaces. Homomorphisms of vector spaces. Homomorphisms and matrices. Systems of linear equations.
Last update: Bečvář Jindřich, doc. RNDr., CSc. (02.05.2005)
 Literature - ---CzechEnglish

I. Satake: Linear Algebra, Marcel Dekker, Inc., New York, 1975.

S. Axler: Linear Algebra Done Right, Springer, New York, 1996.

Last update: BECVAR/MFF.CUNI.CZ (11.05.2008)
 Syllabus - ---CzechEnglish

1. Introduction to basic algebraic structures. Fields, rings, integral domains, groups, permutations; examples.

2. Vector spaces. Linear combinations, generating sets, linear independence, basis, coordinates with respect to a basis, dimension, theorem on the dimension of the join and meet; examples.

3. Homomorphisms of vector spaces. Basic properties of homomorphisms, special types of homomorphisms, the theorem on the dimension of the kernel and the image; examples.

4. Homomorphisms and matrices. The matrix of a homomorphism, compositions of homomorphisms and product of matrices, transformation of coordinates of a vector, rank of a matrix, elementary transformations, methods for calculating the rank of matrix, transformations of matrices, inverse matrix; examples.

5. Systems of linear equations. Solvability, the space of solutions and its dimension, the theorem of Frobenius, Gauss elimination method; problems.

Last update: Bečvář Jindřich, doc. RNDr., CSc. (02.05.2005)