## 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 $M(v_1,\dots,a\cdot v_j+b\cdot w,\dots,v_n)=a\ M(v_1,\dots,v_j,\dots,v_n)+b\ M(v_1,\dots,w,\dots,v_n)$