In functional analysis
, a normal operator
on a Hilbert space H
is a continuous linear operator N
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 Cn.