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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. Euclidean vector space, orthogonality of subspaces, orthonormal bases 2. Angle and distance of subspaces of Euclidean vector spaces, external product, orthogonal product. Aplications in geometry and theory of systems of linear equations 3. Homomorphisms of vector spaces, authomorphisms, projection operator 4. Orthogonal projection operator, orthogonal homomorphism, isomorphism of Euclidean vector spaces. 5. Factor vector spaces. 6. Dual vector spaces. 7. Endomorphisms, ring and linear algebra of endomorphisms. 8. Similarity of square matrices. 9. Minimal and characteristic polynomials of endomorphisms and of matrices. 10. Invariant subspaces of endomorphism. Subspaces associated with eigenvalues of endomorphism 11. Root spaces of endomorphism 12. Invariant subspaces of matrices, Subspaces associated with eigenvalues of matrices, Root subspacves of matrices.
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
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Learning outcomes
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Understand homomorphisms of vector spaces and Euclidean spaces. Understand also theory of linear operators on vector spaces.
1. Knowledge Students describe and define basic elements and relations in linear algebra of euclidean spaces and linear operator theory.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Oral exam, Written exam, Student performance
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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Gantmacher F. R. (1988). Teorija matric. Moskva.
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Hefferon J. (2017). Linear algebra. Colchester.
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Jukl M. (2013). Lekce z lineární algebry. UP Olomouc.
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Jukl M. (2010). Lineární algebra: Homomorfismy a Euklidovské vektorové prostory. VUP Oomouc.
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Jukl M. (2001). Lineární operátory. VUP Olomouc.
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