Alternating Map

A Multilinear Map $f:M^{n}\to N$ is alternating if for all $i\neq j$, if $x_{i}=x_{j}$, then $f(x_{1},\ldots,x_{n})=0$. When specialized to Bilinear Maps, this condition reduces to $f(x,x)=0$.

Properties

• It suffices to show that $x_{i}=x_{i+1}$ implies $f(x_{1},\ldots,x_{n})=0$.