Hermitian adjoint
In mathematics, specifically in operator theory, each linear operator A {\displaystyle A} on an inner product space defines a Hermitian adjoint (or adjoint) operator A ∗ {\displaystyle A^{*}} on that space according to the rule ⟨ A x , y ⟩ = ⟨ x , A ∗ y ⟩ , {\displaystyle \langle Ax,y\rangle =\langle x,A^{*}y\rangle ,} where ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is the inner product on the vector space. The adjoint may also be called the Hermitian conjugate or simply the Hermitian after Charles Hermite.