Předmět Linear Algebra and Analytic Geometry 1 (KMA / WSLA1)
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Top 10 materiálů tohoto předmětu
Materiály tohoto předmětu
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Další informace
Obsah
1. Matrices, operations with matrices.2. Elementary operations, Gauss elimination, rank of a matrix.3. Determinant of the matrix and its properties, methods of calculating the determinant.4. Inverse matrix, properties, methods of calculation.5. Systems of linear equations. Frobenius theorem, inhomogeneous systems, general solution, particular solution.6. Homogeneous systems of linear equations, the fundamental system of solutions.7. The structure of the set of solutions of homogeneous and inhomogeneous equations.8. Vector spaces. Linear dependence and independence of vectors, dimension, bases, linear envelope, representation of a vector in the base, transition matrix.9. Vector subspace, general and parametric equations of subspace.10. Intersection, sum and direct sum of subspaces, the Intersection/Sum Dimension Theorem.11. Linear transformation, isomorphism of vector spaces.12. Linear operator on a vector space, matrix of linear operator, the problem of eigenvalues.
Získané způsobilosti
to know and to understand the basic terms of vector algebrabe able to work with vectors, to perform basic operationsto know and understand linear objects in plane and spaceto know nad understand the finite-dimensional linear vector space and its subspaceto know the affine space and its subspaceto know and understand a linear mapping and its propertiesbe able to apply knowledge to specific examplesbe able to study and orientation in the corresponding literature
Literatura
http://phoenix.inf.upol.cz/esf/materialy.htmSaunders Mac Lane and Garrett Birkhoff. Algebra. ALFA, Bratislava, 1972. Tibor Katriňák et al. Algebra a teoretická aritmetika 1. ALFA, Bratislava, 1985. K. R. Matthews. Elementary linear algebra. Online version, 1998. Halmos, P. R. Linear Algebra Problem Book. Cambridge University Press, 1995. ISBN 0883853221.Krupka, D., Musilová J. Lineární a multilineární algebra. SPN, Praha, 1995. Bedřich Bečvář. Lineární algebra. Matfyzpress, Praha, 2002. Ladislav Bican. Lineární algebra. SNTL, Praha, 1979. Ladislav Bican. Lineární algebra a geometrie. Academia, Praha, 2000. J. Weil et al. Rozpracovaná řešení úloh z vyšší algebry. Academia, Praha, 1987. Serge Lang. Undergraduate Algebra. Springer-Verlag, New York, 1990.
Požadavky
Examination: Combined examination will consist of a written part and then an oral part (It will consist in additional questions related to the written part.) It is possible to gain max. 100 points. The evaluation of the course including the classification is carried out in accordance with the Study and Examination Regulations OU.
Garant
prof. RNDr. Olga Rossi, DrSc.
Vyučující
prof. RNDr. Olga Rossi, DrSc.RNDr. Zuzana Václavíková, Ph.D.RNDr. Zuzana Václavíková, Ph.D.