1. komponenta

Lecture type	Total
Lectures	45
Exercises	60

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: Introduction to finite dimensional vector spaces. Basic notions on linear independence, bases, subspaces, matrices, inverses, determinant.

COURSE DESCRIPTION AND SYLLABUS:
1. Opearions with vectors, addition and scalar multiplication. Colinear an coplanar vectors. Linear combinations, linear independence. Rotations, reflections, orthogonal projections.
2. Linear systems. Solution of linear system. Geometry of the solution set. Matrix form of linear systems. matrices. Eliminations of unknowns as LU factorisation of the coefficient matrix. Determinant of matrices.
3. Linearn systems . Geometry of the solution set. Equivalent systems. Elementary transformations and LU factorization. Matrix form of linear system. Homogeneous systems.
4. Homogeneous systems - structure of the solution set. Linear combination. Matrices: matrices, addition and multiplication of matrices. Vector space Rn.
5. Group. Field. Vector space. Linear independence. Basis. Dimension of vector space. Finite dimensional vector space. Representation of vectors in given basis. Examples of vector spaces.
6. Subspace. Intersection and sum of subspaces.
7. Determinant. Binet - Cauchy theorem. Permutations.
8. Rank of matrix. Elementary transformations. Inverse matrix.
9. Linear systems . Structure of the solution set. Linear manifold. Gauss eliminations. LU factorization.
10. Vector space V3. Vectors as equivalence classes. Addition and scalar multiplication. Basis. Scalar product. Orthonormal basis. Orthogonal projection. Cross product. Mixed product.

Mandatory course - Regular study - Mathematics