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Lecturer(s)
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Cenker Václav, Mgr.
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Botur Michal, doc. Mgr. Ph.D.
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Emanovský Petr, doc. RNDr. Ph.D.
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Course content
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2. Matrices: Operations with matrices, vector space of matrices, ring of square matrices. 3. Determinants: Definition, calculation of determinants. 4. Vector spaces: Subspace, subspace generated by a set, basis, dimension. 5. Systems of equations: Homogeneous and nonhomogeneous systems and their solutions, the Frobenius theorem, Gauss elimination, the Cramer rule. 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.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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Understand bases of linear algebra, to master solving the typical tasks.
3. Aplication Students obtain ability to apply knowledge of linear algebra for solving of particular mathematical problems.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Oral exam, Written exam
Credit: the student has to pass one written test (i.e. to obtain at least half of the possible points in the test). Exam: the student has to understand the subject and be able to prove the principal results.
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Recommended literature
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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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Blažek J. (1985). Algebra a teoretická aritmetika I. SPN Praha.
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Hort D., Rachůnek J. (2003). Algebra I. UP Olomouc.
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Katriňák T. (1985). Algebra a teoretická aritmetika (1). Alfa Bratislava.
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Waerden, L. (1971). Algebra I. Springer-Verlag Berlin, Heidelberg, New York.
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