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 .

Read more about Normal Operator:  Properties, Properties in Finite-dimensional Case, Normal Elements, Unbounded Normal Operators, Generalization

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