Encyclopedia > Normal operator

Article Content

Normal operator

In functional analysis, a normal operator on a Hilbert space H is a continuous linear operator N : H → H which commutes with its hermitian adjoint[?] N^*:

N N^* = N^* N.

The main importance of this concept is that the spectral theorem applies to normal operators.

Examples of normal operators:

Unitary operators (N^* = N^-1)
Hermitian operators (N^* = N)
Normal matrices can be seen as normal operators if one takes the Hilbert space to be Cⁿ.

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia

Search over one million articles, find something about almost anything!

Featured Article

Shoreham, New York

... (0.4 mi²) of it is land and none of the area is covered with water. Demographics As of the census of 2000, there are 417 people, 145 households, and 126 ...