Multilinear functional

Set

context $X$…$\mathcal F$-vector space
context $n\in \mathbb N$
definiendum $M\in \mathrm{MultiLin}(X^n)$
context $ 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 $
postulate $ 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) $

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