Normal operator | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-05-06

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Normal_operator


00:00:57 1 Properties
00:01:12 2 Properties in finite-dimensional case
00:07:41 3 Normal elements of algebras
00:08:34 4 Unbounded normal operators
00:08:57 5 Generalization
00:17:40 6 References
00:18:19 Unbounded normal operators
00:20:11 Generalization



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SUMMARY
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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.