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*.

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}.