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multilinear_functional [2013/08/31 18:44] nikolaj created |
multilinear_functional [2014/03/21 11:11] |
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| - | ===== Multilinear functional ===== | ||
| - | ==== Definition ==== | ||
| - | | @#88DDEE: $X$...$\mathcal F$-vector space | | ||
| - | | @#88DDEE: $n\in \mathbb N$ | | ||
| - | | @#FFBB00: $M\in \mathrm{MultiLin}(X^n)$ | | ||
| - | |||
| - | | @#88DDEE: $ M:X^n \to \mathcal F$ | | ||
| - | |||
| - | $X^n$ being the cartesian product of $n$ instances of the vector space $X$. | ||
| - | |||
| - | | $ a,b\in \mathcal F $ | | ||
| - | | $ v_1,\dots,v_n,w\in X $ | | ||
| - | | $ 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) $ | | ||
| - | |||
| - | ==== Discussion ==== | ||
| - | ==== Context ==== | ||
| - | === Subset of === | ||
| - | [[Function]] | ||
| - | === Requirements === | ||
| - | [[Vector space]] | ||
