[[Linear algebra MOC]]
# Multilinear map

Let $(V_{i})_{i=1}^n$ and $X$ be [[vector space|vector spaces]] (or [[Module|modules]] over a commutative ring).
A **multilinear map** $M$ is a function $M : \prod_{i=1}^n V_{i} \to X$ such that it is [[linear map|linear]] in each argument $V_i$ when all others are held constant. #m/def/linalg 

## See also

- [[Balanced product]] generalizes bilinearity to modules over non-commutative rings.

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#state/tidy | #lang/en | #SemBr