Definition:Hermitian Operator

Definition
Let $H$ be a Hilbert space.

Let $A \in B \left({H}\right)$ be a bounded linear operator.

Then $A$ is said to be self-adjoint or hermitian iff:


 * $A = A^*$

That is, if it equals its adjoint $A^*$.

Also see

 * Hermitian matrices, the finite-dimensional self-adjoint operators