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Lecturer(s)
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Zalabová Lenka, doc. Mgr. Ph.D.
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Course content
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The content of the course is the theory of (abstract) vector spaces. We study properties of vector spaces and linear objects defined on vector spaces. Content of lectures: Vector spaces and subspaces, linear (in)dependence of system of vectors, generating, basis, dimension. Intersection and sum of vector subspaces. Linear map and matrix of linear map in different basis, transizion matrix and transformation of coordinates. Linear forms. Bilinear and quadratic forms. Regulatiry, signature. Sylvester's law of inertia. Spaces with skalar product. Orthogonal/orthonormal systém of vectors. Gramm-Schmidt orthogonalization. Orthogonal projectors. Eigenvectors and eigenvalues of linear transformations. Jordan canonical form. Lectures of practicals: Application of linear algebra and geometry in examples.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book), Individual preparation for exam
- Preparation for classes
- 56 hours per semester
- Class attendance
- 56 hours per semester
- Preparation for exam
- 56 hours per semester
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Learning outcomes
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The goal of the course is (abstract) linear algebra.
Student acquires basic subjects of linear algebra useful in mathematical analysis, geometry and numerical mathematics.
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Prerequisites
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Knowledge of matrix computations on the level of the course UMB551 Linear Algebra.
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Assessment methods and criteria
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Combined exam, Interim evaluation
Active participation in the tutorials and understanding of the theory, learning the system wxmaxima and passing both written and oral parts of the exam (50%).
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Recommended literature
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BICAN, L. Lineární algebra. Praha, SNTL, 1979..
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HALMOS, P.R. Finite-Dimensional Vector Spaces, Springer, 1974..
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Lenka Zalabová. Skripta ke kurzu UMB585 Lineárni algebra II.
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SLOVÁK, J. Lineární algebra. MU Brno, www.math.muni.cz/slovak/Vyuka/la.pdf..
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ZLATOŠ, P. Lineární algebra. FMFI Bratislava, www.thales.doa.fmph.uniba.sk/katc/..
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