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Lecturer(s)
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Pozdílková Alena, Mgr. Ph.D.
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Course content
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1. Relations, mappings, mapping properties, matrix definition, basic properties of matrices, matrix operations. 2. Groups, permutations, fields. 3. Vector spaces, subspaces, linear combinations, linear dependence, and independence. 4. Basis, vector coordinates with respect to the basis, dimensions. 5. Systems of linear equations, Gauss elimination method, matrix rank, Frobenius theorem. 6. Determinants, basic properties, and methods of calculating determinants, Cramer's rule. 7. Regular matrices, matrix representation of row transformations, inverse matrices and calculation methods, adjoint matrix. 8. Linear mapping, image, and kernel, properties of linear mapping, isomorphism. 9. Scalar product, norm, metric. 10. Orthogonal and orthonormal systems, orthogonal basis, complement, and projection. 11. Eigenvalues, characteristic polynomial, eigenvectors, Cayley Hamilton theorem, diagonalizability. 12. Jordan normal form, symmetric matrices, nonnegative matrices, Peron's theorem.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Methods of individual activities, Skills training
- Home preparation for classes
- 13 hours per semester
- Preparation for a credit (assessment)
- 30 hours per semester
- Preparation for an exam
- 50 hours per semester
- Contact teaching
- 52 hours per semester
- Home preparation for classes
- 36 hours per semester
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Learning outcomes
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The aim of the course is to equip the student with basic skills in working with selected knowledge from linear algebra and its applications.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Written examination, Home assignment evaluation, Work-related product analysis
Credit: attendance at seminars with a maximum of 3 unexcused absences + test with at least 50% Exam: written
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Recommended literature
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Abidar,K.M., Magnáš,J.R. Matrix algebra. Cabridge 2005..
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Adibar, K. M., Magnáš J. R. Matrix algebra. Cambridge, 2005.
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Coufal,J. a kol. Učebnice matematiky pro ekonomické fakulty. Victoria Publishing, Praha 1996.. 1996.
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Freidberg,S.H. a kol. Linear algebra. Prentice Hall 2003..
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Kolda S. - Černá M. Úvod do lineární algebry a analytické geometrie. Pardubice, 2004.
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Kolda, S., Černá,M. Matematika - Úvod do lineární algebry a geometrie. Pardubice: Univerzita Pardubice, 2004.
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Meyer, C. D. Matrix Analysis and Applied Linear Algebra. SIAM, 2001.
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Prachař,O., Cabrnochová,R. Průvodce předmětem Matematika. 3.část. Pardubice: Univerzita Pardubice, 2002.
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Rachůnek, J. Algebra a teoretická aritmetika I. Olomouc: UP, 1992.
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Slovák, J. Lineární algebra. Učební texty.. Brno: Masarykova univerzita, 1998.
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Slovák, J. Lineární algebra. Učební texty.. Brno: Masarykova univerzita, 1998.
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