multilinear form

noun2

1. •
   Given a vector space V over a field K of scalars, a mapping Vᵏ → K that is linear in each of its arguments;

   • A multilinear form is said to be degenerate if all its function variables are identical. Thus a degenerate m-multilinear form can more concisely be written as M!f. — 1994
2. •
   a similarly multiply linear mapping Mʳ → R defined for a given module M over some commutative ring R.