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Multilinear functional
Definition
$X$…$\mathcal F$-vector space |
$n\in \mathbb N$ |
$M\in \mathrm{MultiLin}(X^n)$ |
$ 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 $ |
$ 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) $ |