Normal Operator

In mathematics, especially functional analysis, a normal operator on a complex Hilbert space is a continuous linear operator

that commutes with its hermitian adjoint N*:

Normal operators are important because the spectral theorem holds for them. Today, the class of normal operators is well-understood. Examples of normal operators are

• unitary operators:
• Hermitian operators (i.e., selfadjoint operators): ; (also, anti-selfadjoint operators: )
• positive operators:
• normal matrices can be seen as normal operators if one takes the Hilbert space to be .