Let $V$ be a vector space. The $m$-fold exterior power of $V$ is the quotient vector space of the $m$-fold tensor product of $V$ by the subspace generated by the pure tensors \(v_1\otimes\cdots\otimes v_m\) for $v_i \in V$ such that $v_j = v_k$ for some $j\neq k$. It is denoted $\wedge^m(V)$ and the elements are written $v_1\wedge\cdots\wedge v_m$.
Wikidata ID: Q13408581