Vector space/Wedge product/Definition

Let ${\displaystyle {}K}$ be a field, and let ${\displaystyle {}V}$ denote a ${\displaystyle {}K}$-vector space. The ${\displaystyle {}K}$-vector space (constructed in fact) ${\displaystyle {}\bigwedge ^{n}V}$ is called the ${\displaystyle {}n}$-th wedge product (or the ${\displaystyle {}n}$-th exterior power, or exterior product) of ${\displaystyle {}V}$. The mapping

${\displaystyle V^{n}\longrightarrow \bigwedge ^{n}V,(v_{1},\ldots ,v_{n})\longmapsto v_{1}\wedge \ldots \wedge v_{n},}$

is called the universal alternating mapping.