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Lecturer(s)
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Jukl Marek, doc. RNDr. Ph.D.
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Course content
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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.
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Learning activities and teaching methods
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Lecture, Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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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.
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Prerequisites
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Understanding of principles of the linear algebra.
KAG/ALN
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Assessment methods and criteria
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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.
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Recommended literature
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Bican, L. (2009). Lineární algebra a geometrie. Praha: Academia.
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Gantmacher F. R. (1988). Teorija matric. Moskva.
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Havel V., Holenda J. (1984). Lineární algebra. SNTL Praha.
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J. Kopáček. (2001). Matematická analýza pro fyziky II. Matfyzpress.
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JÄNICH K. (1994). Linear algebra. Springer.
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Jukl M. (2000). Bilineární a kvadratické formy. VUP Olomouc.
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JUKL Marek. (2014). Analytická geometrie. Olomouc.
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Lang S. (1993). Introduction to linear algebra. Springer.
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Marková L. (1991). Cvičení z geometrie I. VUP Olomouc.
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Sekanina M. (1988). Geometrie II. SNTL Praha.
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Zlatoš P. (2011). Lineárna algebra a geometria. Marenčin Bratislava.
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