In mathematics, specifically in operator theory, each linear operator A {\displaystyle A} on an inner product space defines a Hermitian 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. Wikipedia