# Definition:Normal 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 normal if and only if:

$\mathbf T^* \mathbf T = \mathbf T \mathbf T^*$

where $\mathbf T^*$ denotes the adjoint of $\mathbf T$.