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Lecturer(s)
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Příhonská Jana, doc. RNDr. Ph.D.
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Course content
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1. Definition and basic properties of affine transformation. 2. Theorem of determiancy, inverse transformation. Affine group, matrix of affine trans-formation. 3. Identical points, characteristic equation. 4. Identical direction. 5. Invariant and identical subspace. 6. Translation. Group of translation. 7. Homothety, group of homothety. 8. Basic affines, their properties. 9. Basic properties of congruent transformation. Group of congruences. 10. Homothetic transformation. Group of homotheties.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Home preparation for classes
- 6 hours per semester
- Preparation for exam
- 28 hours per semester
- Preparation for credit
- 14 hours per semester
- Class attendance
- 42 hours per semester
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Learning outcomes
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Affine transformation, matrix of affine transformation, eigenvectors, invariant and identical subspace, homotetics matrix, invariant and identical direction, homotetics group, basic affinities, group of congruency and similarity.
Affine mappings, matrix of an affine mapping, eigenvectors, invariant and double subspaces, invariant and double directions, homothetic group, basic affinities, groups of congruent and similar mappings.
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Prerequisites
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GE3, GE1
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Assessment methods and criteria
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Oral exam, Written exam
Presence in seminars. Semestral work.
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Recommended literature
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Boček, L. - Šedivý, J.:. Grupy geometrických zobrazení. Praha, SPN, 1986.
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Mída, J. - Dlouhý, Z.:. Vektorová algebra a analytická geometrie. Praha, SPN, 1981.
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Prívratská, J.:. Afinita. Rukopis skript, webové stránky KMD FP TUL. &, &.
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Sekanina, M. - Boček, L. - Kočandrle, M. - Šedivý, J.:. Geometrie I., II. Praha. Praha, SPN, 1986.
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