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This course gives, together with parallel
courses on analysis, a basic course of mathematics
for physicists. Emphasis is given also to
relationship of all these disciplines.
Keywords
linear spaces, dimension, matrices, determinants,
groups and algebras of matrices, eigenvalues,
Jordan normal form.
Last update: Kudrnová Hana, Mgr. (20.05.2019)
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Available on the webpage of the course https://www.karlin.mff.cuni.cz/~smid/pmwiki/pmwiki.php?n=Main.LAproFZS2425 Last update: Šmíd Dalibor, Mgr., Ph.D. (02.10.2024)
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D. Šmíd: Lineární algebra pro fyziky, elektronic text, available on the webpage of the course
K. Výborný, M.Zahradník: Používáme lineární algebru (sbírka řešených příkladů), Karolinum 2002
Other sources available on the webpageof the course. Last update: Šmíd Dalibor, Mgr., Ph.D. (02.10.2024)
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Available on the webpage of the course https://www.karlin.mff.cuni.cz/~smid/pmwiki/pmwiki.php?n=Main.LAproFZS2425 Last update: Šmíd Dalibor, Mgr., Ph.D. (02.10.2024)
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1 Vectors and operations with them, scalar products, maps on vectors.
2 Matrix operations, inversion of a matrix.
3 Systems of linear equations, Gauss elimination method.
4 Groups, vector spaces. Subspaces, linear independence, linear span.
5 Basis, dimension, Steinitz theorem.
6 Rank of a matrix, Frobenius theorem.
7 Linear maps and their matrices, kernel and image, rank-nullity theorem.
8 Coordinates and their transformations, similarity of matrices, trace of a matrix and of a linear map.
9 Permutation and its sign. Determinant and its properties. Expansion along a row and a column.
10 Determinant of a product, inverse matrix formula, Cramer's rule.
11 Eigenvectors and eigenspaces.
12 Block matrices, sum and direct sum of subspaces. Last update: Šmíd Dalibor, Mgr., Ph.D. (02.10.2024)
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