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

Father Damien

... lepers who had virtually nothing to keep them warm or fed. After twelve years of ministering to the patients at the leper colony (see Kalawao County, Hawaii), h ...