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Last update: Mgr. Hana Kudrnová (20.05.2019)
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Last update: Mgr. Lukáš Krump, Ph.D. (16.10.2023)
Available on the webpage of the course https://www.karlin.mff.cuni.cz/~smid/pmwiki/pmwiki.php?n=Main.LAproFZS2324 |
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Last update: Mgr. Dalibor Šmíd, Ph.D. (28.09.2020)
D. Šmíd: Lineární algebra pro fyziky, elektronic scriptum, available on the webpage of the course https://msekce.karlin.mff.cuni.cz/~smid/pmwiki/pmwiki.php?n=Main.LAproFZS2021
K. Výborný, M.Zahradník: Používáme lineární algebru (sbírka řešených příkladů), Karolinum 2002
Other sources available on the webpageof the course. |
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Last update: Mgr. Dalibor Šmíd, Ph.D. (28.09.2020)
Available on the webpage of the course https://msekce.karlin.mff.cuni.cz/~smid/pmwiki/pmwiki.php?n=Main.LAproFZS2021 |
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Last update: Mgr. Dalibor Šmíd, Ph.D. (28.09.2020)
1 Systems of linear equations, Gauss elimination method.
2 Matrix operations, inversion of a matrix.
3 Groups, vector spaces. Subspaces, linear independence, linear span.
4 Basis, dimension, Steinitz theorem.
5 Rank of a matrix, Frobenius theorem.
6 Linear maps and their matrices, kernel and image, rank-nullity theorem.
7 Coordinates and their transformations, similarity of matrices, trace of a matrix and of a linear map.
8 Scalar product, Cauchy-Schwarz inequality.
9 Orthogonal complement, orthogonal projection.
10 Permutation and its sign.
11 Determinant and its properties. Expansion along a row and a column.
12 Determinant of a product, inverse matrix formula, Cramer's rule.
13 Eigenvectors and eigenspaces.
14 Block matrices, sum and direct sum of subspaces. |