Course detail

Linear Algebra and Geometry.

FEKT-SLAGAcad. year: 2005/2006

Polynomials. Matrices and determinants. Systems of linear equations. Vector space, scalar product. Spectral analysis. Affine and Euclidian space. Vector calculus in E3. Analytical geometry.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

RNDr. Břetislav Fajmon, Ph.D.

Department

Department of Mathematics (UMAT)

Learning outcomes of the course unit

The ability to work with determinants, matrices, linear equations in vector spaces.

Prerequisites

It is a course of the non-structured ending study program

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The students will acquire knowledge of linear algebra, especially in: matrix calculus, vector spaces and their applications.

Specification of controlled education, way of implementation and compensation for absences

Not applicable.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Anton,H.:Elementary Linear Algebra,John Wiley, NY 1984
Gantmacher,F.R.:The Theory of Matrices,Chelsea Publ. Comp., NY 1960

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme EI-B3 Bachelor's

    branch B3-KAM , 1. year of study, winter semester, compulsory
    branch B3-EST , 1. year of study, winter semester, compulsory
    branch B3-SEE , 1. year of study, winter semester, compulsory
    branch B3-EVM , 1. year of study, winter semester, compulsory

  • Programme EI-M5 Master's

    branch M5-KAM , 1. year of study, winter semester, compulsory

  • Programme EI-M5 Master's

    branch M5-KAM , 1. year of study, winter semester, compulsory

  • Programme EI-M5 Master's

    branch M5-EST , 1. year of study, winter semester, compulsory

  • Programme EI-M5 Master's

    branch M5-EST , 1. year of study, winter semester, compulsory

  • Programme EI-M5 Master's

    branch M5-SEE , 1. year of study, winter semester, compulsory

  • Programme EI-M5 Master's

    branch M5-SEE , 1. year of study, winter semester, compulsory
    branch M5-EVM , 1. year of study, winter semester, compulsory

  • Programme EI-M5 Master's

    branch M5-EVM , 1. year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hours, compulsory

Teacher / Lecturer

RNDr. Břetislav Fajmon, Ph.D.

Syllabus

Matrices and determinants, operations. Block matrices.
Determinants: basic properties. Laplace theorem.
Linear independence. Rank of a matrix, inverses.
Systems of linear equations. Frobenius theorem.
Vector spaces, subspaces. Basis and dimension.
Coordinates and their transformation. Scalar product.
Orthonormal basis, orthogonalization processus.
Orthogonal projection.
Spectral properties of a matrix.
Diagonalisation of a matrix.
Quadratic forms.
Analytical geometry of linear varieties.
Conics and quadrics.

Fundamentals seminar

26 hours, compulsory

Teacher / Lecturer

RNDr. Břetislav Fajmon, Ph.D.

Syllabus

Polynomials, division. Fundamental theorem of algebra.
Decomposition of rational functions.
Matrices and determinants, block matrices.
Determinants: basic properties, Laplace theorem.
Linear independence. Rank of a matrix. Inverses.
Systems of linear equations.
Vector spaces, subspaces. Basis, dimension.
Coordinates. Transformations. Scalar product.
Orthonormal basis. Orhogonal projection.
Spectral properties of a matrix. Similar matrices.
Diagonalization of matrices. Quadratic forms.
Analytical geometry of linear varieties.
Conics and quadrics.