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multilinear_functional [2013/08/31 19:34] nikolaj |
multilinear_functional [2014/03/21 11:11] (current) |
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| ===== Multilinear functional ===== | ===== Multilinear functional ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $X$...$\mathcal F$-vector space | | + | | @#55CCEE: context | @#55CCEE: $X$...$\mathcal F$-vector space | |
| - | | @#88DDEE: $n\in \mathbb N$ | | + | | @#55CCEE: context | @#55CCEE: $n\in \mathbb N$ | |
| - | | @#FFBB00: $M\in \mathrm{MultiLin}(X^n)$ | | + | | @#FFBB00: definiendum | @#FFBB00: $M\in \mathrm{MultiLin}(X^n)$ | |
| - | | @#88DDEE: $ M:X^n \to \mathcal F$ | | + | | @#55CCEE: context | @#55CCEE: $ M:X^n \to \mathcal F$ | |
| $X^n$ being the cartesian product of $n$ instances of the vector space $X$. | $X^n$ being the cartesian product of $n$ instances of the vector space $X$. | ||
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| | $ 1\le j\le n $ | | | $ 1\le j\le n $ | | ||
| - | | @#55EE55: $ M(v_1,\dots,a\cdot v_j+b\cdot w,\dots,v_n)=a\ M(v_1,\dots,v_j,\dots,v_n)+b\ M(v_1,\dots,w,\dots,v_n) $ | | + | | @#55EE55: postulate | @#55EE55: $ M(v_1,\dots,a\cdot v_j+b\cdot w,\dots,v_n)=a\ M(v_1,\dots,v_j,\dots,v_n)+b\ M(v_1,\dots,w,\dots,v_n) $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| - | ==== Context ==== | + | ==== Parents ==== |
| === Subset of === | === Subset of === | ||
| [[Function]] | [[Function]] | ||
| - | === Requirements === | + | === Context === |
| [[Vector space]] | [[Vector space]] | ||
