multilinear
Let ${V}_{1},{V}_{2},\mathrm{\dots},{V}_{n},W$ be vector spaces^{} over a field $K$. A mapping
$$M:{V}_{1}\times {V}_{2}\times \mathrm{\cdots}\times {V}_{n}\to W$$ 
is called multilinear or $n$linear, if $M$ is linear in each of its arguments.
Notes.

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A bilinear mapping is another name for a $2$linear mapping.

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This definition generalizes in an obvious way to rings and modules.

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An excellent example of a multilinear map is the determinant^{} operation.
Title  multilinear 

Canonical name  Multilinear 
Date of creation  20130322 12:33:05 
Last modified on  20130322 12:33:05 
Owner  rmilson (146) 
Last modified by  rmilson (146) 
Numerical id  10 
Author  rmilson (146) 
Entry type  Definition 
Classification  msc 15A69 
Synonym  multilinearity 
Synonym  multilinear 
Synonym  multilinearity 
Related topic  BilinearForm 
Related topic  BilinearMap 