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)
Základní přednáška pro 1.r. UM a pro 1.r. U FI/SŠ.
Last update: T_KA (18.05.2001)
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)
J. Bečvář: Vektorové prostory I, II, III, SPN, Praha, 1978, 1981, 1982.
J. Bečvář: Sbírka úloh z lineární algebry, SPN, Praha, 1975.
J. Bečvář: Lineární algebra, Matfyzpress, Praha, 2000, 2002.
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)
