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Lecturer(s)
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Krupka Michal, doc. RNDr. Ph.D.
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Peška Patrik, RNDr. Ph.D.
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Kolařík Miroslav, doc. RNDr. Ph.D.
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Trnečková Markéta, Mgr. Ph.D.
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Course content
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1. Binary relations. Functions. Equivalences and decompositions. Equivalences and functions. Closure systems. Basic algebraic structures with 1 and 2 binary operations. 2. Vector spaces and subspaces. Linear dependence and independence. Steinitz theorem on exchange bases. Arithmetic vector spaces. Euclidean vector spaces. Orthogonalization process. 3. Matrices. Operations with matrices. 4. Permutations. Determinants. The rule of Sarrus. Laplace's theorem. Properties of determinants. 5. Systems of linear equations. Rank of matrix. Gaussian elimination. Frobenius theorem. Cramer's rule. Fundamental system of solutions of linear equations. 6. Ring of square matrices. Inverse matrices. Characteristic polynomial of matrix. Eigenvalue of matrix. 7. Linear transformation (homomorphism) of vector spaces. Monomorphism and epimorphism of vector spaces. Coordinate transformations. 8. Applications of linear algebra in computer science.
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Learning activities and teaching methods
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Lecture, Demonstration
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Learning outcomes
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The students become familiar with basic concepts of linear algebra.
1. Knowledge Define basic concepts, describe and apply basic methods of linear algebra.
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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, Student performance
Active participation in class. Completion of assigned homeworks. Passing the oral exam.
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Recommended literature
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Bečvář, J. (2010). Lineární algebra. Praha: Matfyzpress.
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Bican, L. (2009). Lineární algebra a geometrie. Praha: Academia.
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Halmos P.R. (1995). Linear Algebra Problem Book. Cambridge University Press.
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Chajda, I. (1999). Úvod do algebry. Olomouc: Univerzita Palackého.
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Jukl, M. (2010). Lineární algebra: euklidovské vektorové prostory : homomorfizmy vektorových prostorů. Olomouc: Univerzita Palackého v Olomouci.
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