|Course title||Analytical Geometry|
|Organizational form of instruction||Lecture + Exercise|
|Level of course||Bachelor|
|Year of study||not specified|
|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|
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)|
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.
|Study plans that include the course|