Let V₁,V₂,⋯,V_k,W be vector spaces over the same field. Generalizing the notion of bilinear, a multilinear map f:V₁×V₂×⋯×V_k → W is a function f(v₁,…,v_k) which is linear (see linear map) in each variable v_i. As an example, the determinant is multilinear in its rows (and likewise in its columns).