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Normal operator

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

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