In mathematics, especially functional analysis, a normal operator on a complex Hilbert space H is a continuous linear operator N : H → H that commutes with its hermitian adjoint N*, that is: NN* = N*N. Normal operators are important because the spectral theorem holds for them. The class of normal operators is well understood. Examples of normal operators are * unitary operators: N* = N−1 * Hermitian operators (i.e., self-adjoint operators): N* = N * Skew-Hermitian operators: N* = −N * positive operators: N = MM* for some M (so N is self-adjoint). A normal matrix is the matrix expression of a normal operator on the Hilbert space Cn. (Wikipedia).
Normal operators. Characterization of normal operators by ||Tv|| = ||T*v|| for all v. Eigenvectors of a normal operator corresponding to distinct eigenvalues are orthogonal.
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