Science Fair Project Encyclopedia
Unitary operator
In functional analysis, a unitary operator is a bounded linear operator U on a Hilbert space satisfying
- U*U=UU*=I
where I is the identity operator. This property is equivalent to any of the following:
- U is a surjective isometry
- U is surjective and preserves the inner product on the Hilbert space, so that for all vectors x and y in the Hilbert space,
Unitary matrices are precisely the unitary operators on finite-dimensional Hilbert spaces, so the notion of a unitary operator is a generalisation of the notion of a unitary matrix.
Unitary operators implement isomorphisms between operator algebras.
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details