Alternating multilinear map

In mathematics, more specifically in multilinear algebra, an alternating multilinear map is a multilinear map with all arguments belonging to the same space (e.g., a bilinear form or a multilinear form) that is zero whenever any two adjacent arguments are equal.

The notion of alternatization (or alternatisation in British English) is used to derive an alternating multilinear map from any multilinear map with all arguments belonging to the same space.

A multilinear map of the form ${\displaystyle f\colon V^{n}\to W}$ is said to be alternating if ${\displaystyle f(x_{1},\ldots ,x_{n})=0}$ whenever there exists ${\textstyle 1\leq i\leq n-1}$ such that ${\displaystyle x_{i}=x_{i+1}.}$

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