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Adjoint operator

For

T \in L (H)

, the adjoint

T^{*}

is the unique bounded operator satisfying

⟨ T x, y ⟩ = ⟨ x, T^{*} y ⟩ .

Riesz representation applied for each

y

proves existence; in an orthonormal basis its matrix is the conjugate transpose of the matrix of

T

.

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