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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