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antisymmetric_multilinear_functional [2013/08/31 18:55] nikolaj created |
antisymmetric_multilinear_functional [2014/03/21 11:11] |
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| - | ===== Antisymmetric multilinear functional ===== | ||
| - | ==== Definition ==== | ||
| - | | @#88DDEE: $X$...$\mathcal F$-vector space | | ||
| - | | @#88DDEE: $n\in \mathbb N$ | | ||
| - | | @#FFBB00: $M\in \mathrm{SymMultiLin}(X^n)$ | | ||
| - | |||
| - | | @#88DDEE: $M\in \mathrm{MultiLin}(X^n)$ | | ||
| - | |||
| - | | $ v_1,\dots,v_n\in X $ | | ||
| - | | $ 1\le i<j\le n $ | | ||
| - | |||
| - | | @#55EE55: $ M(v_1,\dots,v_i,\dots,v_j,\dots,v_n)=-M(v_1,\dots,v_j,\dots,v_i,\dots,v_n) $ | | ||
| - | |||
| - | ==== Discussion ==== | ||
| - | ==== Context ==== | ||
| - | === Subset of === | ||
| - | [[Multilinear functional]] | ||
