Lecturer(s)


Juklová Lenka, RNDr. Ph.D.

Jukl Marek, doc. RNDr. Ph.D.

Course content

1.Characteristic polynomials of matrices, eigenvalues and eigenvectors, characteristic subspaces, minimal polynomials. Jordan cells, Jordan canonical form of a matrix. 2.Linear and bilinear forms, singular vectors, polar bases. 3.Scalar products on vector spaces. The GrammSchmidt orthogonalization process for polar bases. 4.Quadratic and bilinear forms, polar bases, signatures. 5.Diagonalisation of the matrix of a real quadratic form. 6.Conics in the Euclidean plane. Canonical equations. 7.Lines and conics. 8.Metric and affine classification of conics, affine and metric invariants. 9.Quadratic surfaces in a 3dimmensional Euclidean space (quadrics). Canonical equations. 10.Lines and quadrics. Planes and quadrics. 11.Metric and affine classification of quadrics.

Learning activities and teaching methods

Lecture, Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)

Learning outcomes

Understand principles of the analytical geometry and the multilinear algebra, to master solving the typical problems.
1. Knowledge List of the fundamental knowledge from the analytical geometry for students of the physical courses.

Prerequisites

Understanding of the principles of the linear algebra.

Assessment methods and criteria

Oral exam, Written exam
Credit: the student has to pass two written tests (i.e. to obtain at least half of possible points in each test). Exam: the student has to understand the subject and be able to use the theory in applications.

Recommended literature


Bican L. (1979). Lineární algebra. SNTL Praha.

Gantmacher F. R. (1988). Teorija matric. Moskva.

Havel V., Holenda J. (1984). Lineární algebra. SNTL Praha.

JÄNICH K. (1994). Linear algebra. Springer.

Janyška J., Sekaninová A. (1996). Analytická geometrie kuželoseček a kvadrik. PřF MU Brno.

Jukl M. (2006). Analytická geometrie kuželoseček a kvadrik. UP Olomouc.

Kopáček J. (2003). Matematická analýza pro fyziky II, IV. Matfyzpress, Praha.

Lang S. (1993). Introduction to linear algebra. Springer.

Sekanina M. (1988). Geometrie II. SNTL Praha.
