Let $V$ be an $n$-dimensional vector space and let $T:V\to V$ be a linear transformation. The adugate of $T$ is \(\text{adj}(T):V\to V\) the unique linear transformation such that for all $v \in V$ and all $w \in \wedge^{n-1}(V)$ the $n-1$-fold exterior product of $V$, \(\text{adj}(T)(v) \wedge w = v \wedge (\wedge^{n-1}(T)(w)) \in \wedge^n(V).\)
Wikidata ID: Q225107