FI:M003 Linear Algebra and Geometry I

M003 Linear Algebra and Geometry I

Faculty of Informatics
Autumn 1995

Extent and Intensity

0/0. 4 credit(s). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).

Teacher(s)

prof. RNDr. Jan Slovák, DrSc. (lecturer)

Guaranteed by

Contact Person: prof. RNDr. Jan Slovák, DrSc.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

Syllabus

Scalars, vectors and matrices: Properties of real and complex numbers, vector spaces and their examples, $R^n$ and $C^n$, multiplication of matrices, systems of linear eguations, Gauss elimination, computation of inverse matrices.
Vector spaces - basic notions: Linear combinations, linear independence, basis, dimension, vector subspaces, intersections and sums of subspaces, coordinates.
Linear mappings: Definition, kernel and image, linear isomorphism, matrix of linear mapping in given bases, transformation of coordinates.
Systems of linear equations: Properties of sets of solutions, rank a matrix, existence of solutions.
Determinants: Permutations, definition and basic properties of determinants, computation of inverse matrices, application to systems of linear equations.
Affine subspaces in $R^n$: Definition, parametric and implicit description, affine mapping.

Language of instruction

Czech