Editing Bra–ket notation (section)

===Hermitian conjugate operator===
{{main|Hermitian conjugate}}
Just as kets and bras can be transformed into each other (making {{math|{{ket|''ψ''}}}} into {{math|{{bra|''ψ''}}}}), the element from the dual space corresponding to {{math|''A''{{ket|''ψ''}}}} is {{math|{{bra|''ψ''}}''A''<sup>†</sup>}}, where {{math|''A''<sup>†</sup>}} denotes the Hermitian conjugate (or adjoint) of the operator {{math|''A''}}. In other words,
<math display="block"> |\phi\rangle = A |\psi\rangle \quad \text{if and only if} \quad \langle\phi| = \langle \psi | A^\dagger \,.</math>

If {{math|''A''}} is expressed as an {{math|''N'' × ''N''}} matrix, then {{math|''A''<sup>†</sup>}} is its conjugate transpose.