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Antisymmetric multilinear functional

Definition

$X$…$\mathcal F$-vector space
$n\in \mathbb N$
$M\in \mathrm{SymMultiLin}(X^n)$
$M\in \mathrm{MultiLin}(X^n)$
$ v_1,\dots,v_n\in X $
$ 1\le i<j\le n $
$ 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

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