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leibniz_formula_for_determinants [2013/09/17 22:53] nikolaj old revision restored (2013/09/17 22:43) |
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| - | ===== Leibniz_formula for determinants ===== | + | ===== Leibniz formula for determinants ===== |
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $n\in \mathbb N$ | | + | | @#55CCEE: context | @#55CCEE: $n\in \mathbb N$ | |
| - | | @#88DDEE: $R$ ... abelian ring | | + | | @#55CCEE: context | @#55CCEE: $R$ ... abelian ring | |
| - | | @#FFBB00: $ \mathrm{det}_n:\mathrm{SquareMatrix}(n,R)\to R$ | | + | | @#FFBB00: definiendum | @#FFBB00: $ \mathrm{det}_n:\mathrm{SquareMatrix}(n,R)\to R$ | |
| - | | @#FFBB00: $ \mathrm{det}_n(A):=\sum_{j_1,\dots,j_n}^n\varepsilon_{j_1,\dots,j_n}\cdot \prod_{k=1}^n A_{k,j_k}$ | | + | | @#FFBB00: definiendum | @#FFBB00: $ \mathrm{det}_n(A):=\sum_{j_1,\dots,j_n}^n\varepsilon_{j_1,\dots,j_n}\cdot \prod_{k=1}^n A_{k,j_k}$ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| This function concides with the implicitly defined determinant of [[Determinant]], if the matrices are taken to be linear operators in the usual way. | This function concides with the implicitly defined determinant of [[Determinant]], if the matrices are taken to be linear operators in the usual way. | ||
| + | === Reference === | ||
| + | Wikipedia: [[http://en.wikipedia.org/wiki/Leibniz_formula_for_determinants|Leibniz formula for determinants]] | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| - | [[Matrix ring]] | + | [[Matrix ring]], |
| - | === Requirements === | + | [[Determinant via multilinear functionals]], |
| - | [[Determinant]], | + | |
| [[Infinite series]] | [[Infinite series]] | ||
