Course: Analytical Geometry

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Course title Analytical Geometry
Course code KAG/AGN
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • 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 Gramm-Schmidt 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 3-dimmensional 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.
Understanding of 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.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science General Physics and Mathematical Physics (1) Physics courses 1 Summer
Faculty of Science Optics and Optoelectronics (1) Physics courses 1 Summer