Conjugate transpose: Difference between revisions

Revision as of 10:12, 21 June 2004

Revision as of 10:14, 21 June 2004

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:<math>(A^*)[i,j] = \overline{A[j,i]}</math>

for 1 &le; ''i'' &le; ''n'' and 1 &le; ''j'' &le; ''m''.

This is a particular case of the '''[[Hermitian conjugate]]''' (sometimesometimes called [[Hermitian adjoint]] or just '''adjoint''') [[linear operator]].

==Example==

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:<math> \lang \phi | (A|\psi) \rang = \lang (A^{\dagger}\phi) | \psi) \rang </math>

The term [[Hermitian conjugate transpose]] is used since if <math> A = A^{\dagger} </math> than A is called an '''[[Hermitian]] operator'''.