Let $(V,F)$ and $(W,F)$ be vector spaces over the same field with respective inner products $\langle\cdot,\cdot\rangle_V$ and $\langle\cdot,\cdot\rangle_V$. The adjoint of a linear transformation $T:V\to W$ is the linear transformation $T^*: W \to V$ such that \(\langle T(v), w\rangle_W = \langle v, T^*(w)\rangle_V\) for all $v \in V$ and $w \in W$.
Wikidata ID: Q2858846