# Normal operator

In

functional analysis, a

**normal operator** on a

Hilbert space *H* is a

continuous linear operator *N* :

*H* →

*H* that

commutes with its hermitian adjoint

*N*^{*}:

*N* *N*^{*} = *N*^{*} *N*.

The main importance of this concept is that the

spectral theorem applies to normal operators.

Examples of normal operators:

- Unitary operators (
*N*^{*} = *N*^{ −1})
- Hermitian operators (
*N*^{*} = *N*)
- Normal matrices can be seen as normal operators if one takes the Hilbert space to be
**C**^{n}.