Normal operator
From Wacklepedia - 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.