# Definition:Hermitian Operator

## Definition

Let $\HH$ be a Hilbert space.

Let $\mathbf T: \HH \to \HH$ be a bounded linear operator.

Then $\mathbf T$ is said to be Hermitian if and only if:

$\mathbf T = \mathbf T^*$

That is, if and only if it equals its adjoint $\mathbf T^*$.

## Also known as

A Hermitian operator is also known as a self-adjoint operator.

## Also see

• Results about Hermitian operators can be found here.

## Source of Name

This entry was named for Charles Hermite.