> [!NOTE] Definition (Multilinear map) > Let $(V_{i})_{i=1}^{n}$ and $W$ be vector spaces for $n\in \mathbb{N}_{\geq 0}.$ Then $\varphi: V_{1} \times \dots \times V_{n} \to W$is a multilinear map if for each $i,$ if all the other $v_{i}$ are held constant the $\varphi(v_{1},\dots,v_{i}, \dots,v_{n})$ is a linear function in $v_{i}.$