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Lecturer(s)
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Křížek Jan, Mgr.
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Vaněk Vladimír, Mgr. Ph.D.
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Jukl Marek, doc. RNDr. Ph.D.
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Broušek Martin, Mgr.
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Kurač Zbyněk, Mgr.
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Course content
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1. Euclidean vector space 2. Orthogonality, angle and distance in Euclidean vector spaces 3. External product, orthogonal product. 4. Homomorphisms of vector spaces 5. Vector space of homomorphisms 6. Endomorphisms of vector space 7. Homomorphisms of Euclidean vector spaces. 8. Vector subspaces associated with eigenvalues of endomorphism 9. Factor vector spaces. 10. Dual vector spaces. 11. Generalized inverse of a matrix 12. Moore-Penrose homomorphism
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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Understand homomorphisms of vector spaces and the Euclidean spaces. Understand also generalized inverse and Moor-Penrose pseudoinverse.
1. Knowledge Students describe and define basic elements and relations in linear algebra of euclidean spaces and quadratic forms and g-inversion of matrices.
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Prerequisites
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unspecified
KAG/LA1S
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Assessment methods and criteria
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Oral exam, Written exam
Credit: The student has to participate in seminars actively and has to pass a written test. Exam: The student has to understand the subject and be able to prove the principal results. The student has to be able to solve problems.
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Recommended literature
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Bican L. (1979). Lineární algebra. SNTL Praha.
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Birkhoff G., MacLane S. (1979). Prehľad modernej algebry. Alfa Bratislava.
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Gantmacher F. R. (1988). Teorija matric. Moskva.
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I., Chajda. (1999). Úvod do algebry. UP Olomouc.
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Jukl M. (2006). Lineární algebra: Homomorfismy a Euklidovské vektorové prostory. VUP Oomouc.
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Rao K., Mitra K. S. (1971). Generalized Inverse of Matrices and Its Application. New York.
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