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Lecturer(s)
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Pozdílková Alena, Mgr. Ph.D.
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Marek Jaroslav, Mgr. Ph.D.
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Vozáb Jaroslav, Mgr.
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Rulićová Iva, RNDr.
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Course content
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Binary relations, mapping and their properties. Vector spaces over field numbers R, C. Vector subspaces, linear manifolds, vector spacec R^n, C^n. Linear dependence and independece, bases, dimension. Elements of matrix calculus, matrix addition, scalar and matrix multiplication. Elementary matrix transformations, rank. Permutations, determinants and their basic properties. Expansion of determinants with respect to row/column. Determinant of matrix product. Regular and non-regular matrices, ring of square matrices, inverse matrix and its evaluation. Systems of linear equations over R. Components with respect to basis, coordinate transformations. Euclidean vector spaces, orthogonal bases, orthogonalization method, orthogonal complement, Gramm matrices. Vector calculus in 3-dimensional Euclidean space, inner and cross products. Review of analytical geometry in 3-dimensional Euclidean space, equations of lines and planes.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Methods of individual activities, Skills training
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Learning outcomes
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The aim of the course is to provide the students with basic acquirements to use the selected knowledge from linear algebra and its applications.
A student acquires a satisfactory view of some topics of the linear algebra. The obtained knowledge enable students to use the mathematical appliance in various areas of mathematics and in special courses of their specialization.
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Prerequisites
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The course demands the knowledge of basic algebraic and geometric topics of mathematics in secondary schools.
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Assessment methods and criteria
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Written examination, Home assignment evaluation, Work-related product analysis
Credit requirements: active participation in seminars with at most three hours absent, and at least 50% success in written test. The course is completed by written exam, at least 55% of success is required. An oral form of the exam is optional, upon a student's request.
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Recommended literature
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Abidar,K.M., Magnáš,J.R. Matrix algebra. Cabridge 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. Matematika - Úvod do lineární algebry a geometrie. 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. Univerzita Pardubice, 2002.
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Slovák, J. Lineární algebra. Učební texty.. Brno Masarykova univerzita, 1998.
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