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determinant_via_multilinear_functionals [2013/09/17 23:21] nikolaj |
determinant_via_multilinear_functionals [2014/03/21 11:11] (current) |
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| ===== Determinant via multilinear functionals ===== | ===== Determinant via multilinear functionals ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $V$ ... finite dimensional $\mathcal F$-vector space | | + | | @#55CCEE: context | @#55CCEE: $V$ ... finite dimensional $\mathcal F$-vector space | |
| - | | @#FFBB00: $\mathrm{det}:L(V,V)\to \mathcal F$ | | + | | @#FFBB00: definiendum | @#FFBB00: $\mathrm{det}:L(V,V)\to \mathcal F$ | |
| - | | @#DDDDDD: $n\equiv \mathrm{dim}(V)$ | | + | | @#DDDDDD: range | @#DDDDDD: $n\equiv \mathrm{dim}(V)$ | |
| | $M\in \mathrm{MultiLin}(V^n)$ | | | $M\in \mathrm{MultiLin}(V^n)$ | | ||
| | $ v_1,\dots,v_n\in V $ | | | $ v_1,\dots,v_n\in V $ | | ||
| | $A\in L(V,V)$ | | | $A\in L(V,V)$ | | ||
| - | | @#55EE55: $ M(A\ v_1,\dots,A\ v_n) = \mathrm{det}(A)\cdot M(v_1,\dots,v_n) $ | | + | | @#55EE55: postulate | @#55EE55: $ M(A\ v_1,\dots,A\ v_n) = \mathrm{det}(A)\cdot M(v_1,\dots,v_n) $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
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| Wikipedia: [[http://en.wikipedia.org/wiki/Determinant|Determinant]] | Wikipedia: [[http://en.wikipedia.org/wiki/Determinant|Determinant]] | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| [[Multilinear functional]], [[Linear operator algebra]], [[Vector space dimension]] | [[Multilinear functional]], [[Linear operator algebra]], [[Vector space dimension]] | ||
