Multilinear map
In linear algebra, a multilinear map is a function of several variables that is linear separately in each variable. More precisely, a multilinear map is a function f : V 1 × ⋯ × V n → W , {\displaystyle f\colon V_{1}\times \cdots \times V_{n}\to W{\text{,}}} where V 1 , … , V n {\displaystyle V_{1},\ldots ,V_{n}} ( n ∈ Z ≥ 0 {\displaystyle n\in \mathbb {Z} _{\geq 0}} ) and W {\displaystyle W} are vector spaces (or modules over a commutative ring), with the following property: for each i {\displaystyle i} , if all of the variables but v i {\displaystyle v_{i}} are held constant, then f ( v 1 , … , v i , … , v n ) {\displaystyle f(v_{1},\ldots ,v_{i},\ldots ,v_{n})} is a linear function of v i {\displaystyle v_{i}} .