A normal operator is a bounded linear operator on a Hilbert space that commutes with its adjoint, meaning that for an operator \(T\), it holds that \(T^*T = TT^*\). This property leads to several important characteristics, including the existence of an orthonormal basis of eigenvectors and the applicability of the spectral theorem. Normal operators encompass self-adjoint operators, unitary operators, and other types of operators that play a vital role in functional analysis.
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