Normal operator
From Biocrawler, the free encyclopedia.
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 Cn.
