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Adjoint Matrix

Definition

The word adjoint has a number of related meanings. In linear algebra, it refers to the conjugate transpose and is most commonly denoted A^H. The analogous concept applied to an operator instead of a matrix, sometimes also known as the Hermitian conjugate, is most commonly denoted using dagger notation A^†. The adjoint operator is very common in both Sturm-Liouville theory and quantum mechanics. For example, Dirac denotes the adjoint of the bra vector 〈P right bracketing bar α as α^† left bracketing bar P〉, or α^_ left bracketing bar P〉.

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