Adjoint Operator

linear-algebra

Definition

Adjoint Operator

Let $T:\mathcal{H}\to \mathcal{H}$ be a linear operator on a complex inner product space $\mathcal{H}$. The adjoint of $T$ is the unique operator $T^{†}$ satisfying

$$⟨Tx,y⟩=⟨x,T^{†}y⟩\forall x,y\in \mathcal{H}$$

Sometimes $T^{†}$ is denoted as $T^{\ast }$.