Adjoint Operator Homework: Clarifying Complex Conjugates

[PhysicsGente]

Homework Statement

Hello,

I need some things clarified before I can do my homework. They have to do with the adjoint operator. Say I have an operator P and its adjoint is P(dagger). I noticed that the complex conjugate of the adjoint gives back the operator. Does that mean the adjoint is just the complex conjugate?

 

[vela]

No, that's not true. If you represent the operator as a matrix, you'll find the adjoint is the conjugate of the transposed matrix. It's not simply the conjugate.