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Linear algebra I (CŽV) - NMUM802

Title:	Lineární algebra I (CŽV)
Guaranteed by:	Department of Mathematics Education (32-KDM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Is provided by:	NMUM103

Guarantor:	doc. RNDr. Jindřich Bečvář, CSc. RNDr. Martina Škorpilová, Ph.D.
Classification:	Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Incompatibility :	NMUM103, NUMP003
Interchangeability :	NMUM103, NUMP003

Annotation -

Last update: JUDr. Dana Macharová (10.10.2012)

Basic linear algebra course for prospective teachers.

Literature -

Last update: JUDr. Dana Macharová (10.10.2012)

Syllabus -

Last update: JUDr. Dana Macharová (10.10.2012)

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

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.

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

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.