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Lecturer(s)
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Heckenbergerová Jana, Mgr. Ph.D.
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Pozdílková Alena, Mgr. Ph.D.
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Course content
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Euclidean vector spaces: orthogonalization, orthogonal and unitary matrices, orthogonal projection, decompositions of matrices and their applications. Linear mappings of vector spaces: matrix of linear mapping, automorphisms, projections, orthogonal mappings, quotient vector spaces. Linear operators: similar matrices, minimal and characteristic polynomial, polynomial matrices, Cayley-Hamilton theorem, invariant subspaces, eigen-subspaces, canonical Jordan form and its applications. Bilinear and quadratic forms.
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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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To afford students more remarkable knowledge on vector spaces, matrix theory and their use in practices.
Students will obtain survey of the linear algebra which unable them to home study new trends in their professional field in future.
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Prerequisites
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Prerequisite for successful mastering of this subject is knowledge of linear algebra within the range the basic course of mathematics.
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Assessment methods and criteria
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Written examination, Discussion, Systematic monitoring
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 an oral exam; student should demonstrate an active knowledge of predefined topics.
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Recommended literature
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Abadir, K.M., Magnus, J.,R. Matrix Algebra. Cambridge, 2005.
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Friedberg,S.H., Insel,A.J.,Spence,L.E. Linear Algebra. Prentice Hall, 2003.
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Gelfand, I. M. Lineární algebra. Praha, 1953.
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Halmos, P. R. Finite-dimensional vector spaces. New York, 1958.
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Meyer, C. D. Matrix Analysis and Applied Linear Algebra. SIAM, 2001.
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Nicholson, K.W. Linear algebra with aplications. Washington, 1990.
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