Linear Algebra I - NUMP003
Title: Lineární algebra I
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
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
Guarantor: doc. RNDr. Jindřich Bečvář, CSc.
Classification: Mathematics > Algebra
Teaching > Mathematics
Incompatibility : NALG001, NALG002, NMAI057, NMAI058
Interchangeability : NALG001, NMUE024, NMUM103
Is incompatible with: NMAF012, NMUM103, NMUM802, NALG003, NMAI045, NMAF031
Is interchangeable with: NMAF031, NMUM802, NMUM103, NMUE024
Opinion survey results   Examination dates   Schedule   Noticeboard   
Annotation -
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 -

S. Lang: Linear Algebra, Addison-Wesley Publishing Company-Reading, 1966.

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 -

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)