Normal operator

From Exampleproblems

In functional analysis, a normal operator on a Hilbert space H is a continuous linear operator that commutes with its hermitian adjoint 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.