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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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Lecture topics by week of the semester: 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. 6. Matrix rank, Frobenius theorem. 7. Determinants, basic properties, and methods of calculating determinants, Cramer's rule. 8. Regular matrices, matrix representation of row transformations, inverse matrices and calculation methods, adjoint matrix. 9. Linear mapping, image, and kernel, properties of linear mapping, isomorphism. 10. Scalar product, norm, metric. 11. Orthogonal and orthonormal systems, orthogonal basis, complement, and projection. 12. Eigenvalues, characteristic polynomial, eigenvectors, Cayley Hamilton theorem, diagonalizability. 13. Jordan normal form, symmetric matrices, nonnegative matrices, Perron's theorem. The content of the exercises corresponds to the topics of the lectures.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Skills training
- Contact teaching
- 24 hours per semester
- Home preparation for classes
- 88 hours per semester
- Preparation for a credit (assessment)
- 33 hours per semester
- Preparation for an exam
- 35 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 and selected knowledge in the field of linear algebra and its applications.
After completing the course, the student demonstrates knowledge of selected parts of linear algebra and is able to use them practically.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Written examination
Credit: test with at least 50 % Exam: written
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Recommended literature
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ABADIR, Karim M. a MAGNUS, Jan R. Matrix algebra. Econometric exercises, 1. New York: Cambridge University Press, 2005. ISBN 978-0-521-53746-0.
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COUFAL, Jan a kol. Učebnice matematiky pro ekonomické fakulty. Praha: Victoria Publishing, 1996. ISBN 80-7187-148-6.
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FRIEDBERG, Stephen H.; INSEL, Arnold J. a SPENCE, Lawrence E. Linear algebra. 4th ed. Upper Saddle River: Pearson Education, 2003. ISBN 978-0-13-008451-4.
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KOLDA, Stanislav a ČERNÁ, Milada. Matematika - Úvod do lineární algebry a analytické geometrie. Vyd. 10. Pardubice: Univerzita Pardubice, 2007. ISBN 978-80-7395-033-0.
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PRACHAŘ, Otakar a CABRNOCHOVÁ, Renáta. Průvodce předmětem matematika I. (3. část), Úlohy z lineární algebry, analytické geometrie a z nekonečných řad. Vyd. 4. Pardubice: Univerzita Pardubice, 2010. ISBN 978-80-7395-329-4.
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RACHŮNEK, Jiří. Algebra a teoretická aritmetika I. 3. přeprac. vyd. Olomouc: Rektorát Univerzity Palackého, 1992. ISBN 80-7067-050-9.
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SLOVÁK, Jan. Lineární algebra [učební text online]. Brno: Masarykova univerzita, 1998.
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