\begin{definition}[Definition:Normal Operator]
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''' {{iff}}:
:$\mathbf T^* \mathbf T = \mathbf T \mathbf T^*$
where $\mathbf T^*$ denotes the adjoint of $\mathbf T$.
\end{definition}