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leibniz_formula_for_determinants [2013/09/17 23:22] nikolaj |
leibniz_formula_for_determinants [2014/03/21 11:11] |
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- | ===== Leibniz formula for determinants ===== | ||
- | ==== Definition ==== | ||
- | | @#88DDEE: $n\in \mathbb N$ | | ||
- | | @#88DDEE: $R$ ... abelian ring | | ||
- | | @#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}$ | | ||
- | |||
- | ==== Discussion ==== | ||
- | 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 ==== | ||
- | === Requirements === | ||
- | [[Matrix ring]] | ||
- | === Requirements === | ||
- | [[Determinant via multilinear functionals]], | ||
- | [[Infinite series]] |