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Lecturer(s)
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Botur Michal, doc. Mgr. Ph.D.
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Emanovský Petr, doc. RNDr. Ph.D.
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Ševčík Petr, Mgr.
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Lachman Dominik, Mgr.
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Kurač Zbyněk, Mgr.
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Vítková Lenka, Mgr. Ph.D.
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Křížek Jan, Mgr.
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Riemel Tomáš, Mgr.
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Cenker Václav, Mgr.
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Course content
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1. Introduction: Elements of mathematical logic, sets, relations, mappings, algebraic structures. 2. Matrices: Operations with matrices, vector space of matrices, ring of square matrices. Determinants: Definition, calculation of determinants. 3. Systems of equations: Homogeneous and nonhomogeneous systems and their solutions, the Frobenius theorem, Gauss elimination, the Cramer rule. 4. Vector spaces: Subspace, subspace generated by a set, basis, dimension. 5. Affine spaces, affine coordinates, affine subspaces, expression of subspaces by means of equations, relative position of affine subspaces. 6. Homomorphisms and isomorphisms of vector spaces: Arithmetical vector spaces and their importance for description of vector spaces, coordinates of vectors according to a given basis, transformation of coordinates as consequense of change of basis, matrix of transformation, matrix of endomorphism. 7. Inner product spaces: Inner product, length of a vector, angle between vectors, orthogonal and orthonormal basis, Gram-Schmidt orthogonalization, isomorphism of inner product spaces. 8.Oriented affine lines, ordered affine lines, half-lines, abscissas. Oriented affine spaces, half-spaces. 9. Euclidean spaces, metric, distance of subspaces. Angle of subspaces.
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Learning activities and teaching methods
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Lecture, Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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Understand the principles linear algebra.
1. Knowledge List of the fundamental knowledge from the algebra for students of the physical courses.
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Prerequisites
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Understanding of mathematics on secondary school level.
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Assessment methods and criteria
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Oral exam, Written exam
Credit: the student has to participate in seminars actively and do homework assignments. He/She has to pass a written test successfuly. Exam: the student has to pass a written part successfuly. He/She has to understand the problems and interpret them correctly.
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Recommended literature
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Bartsch, H. J. (1996). Matematické vzorce. Praha: Mladá fronta.
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Bican, L. (2000). Lineární algebra a geometrie. Praha, Academia.
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Bican L. (1979). Lineární algebra. SNTL Praha.
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Borůvka O. (1971). Základy teorie matic. Academia Praha.
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Hort D., Rachůnek, J. (2005). Algebra I. Olomouc.
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Jukl M. (2006). Lineární algebra. UP Olomouc.
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JUKL Marek. (2014). Analytická geometrie. Olomouc.
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Klucký D. (1989). Kapitoly z lineární algebry I. VUP Olomouc.
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Rektorys K. (1981). Přehled užité matematiky. SNTL Praha.
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