Multilinear

A function $T:V^n\to W$ is multilinear if it is linear in each of its n inputs $T(v_1,\dots ,a{v}_i+b{v}_i,\dots v_n)=aT(v_1,\dots ,v_n)+bT(v_i,\dots ,v_n)$

Intuition

A regular linear transform is like 1, whereas a multilinear transform is like n, it takes n inputs rather than one input. All linear transformations are multilinear transformations.