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,

\langle Ux, Uy \rangle = \langle x, y \rangle.

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.

<< Previous

Word Browser

Next >>

iso 3166 2:2002 12 10
iso 3166 2:es
hugh blair
american conference of governmental industrial hygienists
the mind is a terrible thing to taste
polish hip hop
fisher ames
robert ferguson
psalm 69: the way to succeed and the way to suck eggs
percentile rank
iso 3166 2:et

john home
george william forbes
standardized test
margaret woffington
worker safety and health
sand wedge
ground state
augustin daly
william franklin
ada rehan
iso 3166 2:in

ann gilbert
iso 3166 2:kh
john brougham
iso 3166 2:kp
william evans burton
james william wallack
iso 3166 2:2002 08 20
john lester wallack
iso 3166 2:kz
iso 3166 2:la
iso 3166 2:md

iso 3166 2:mu
iso 3166 2:ro
francis james child
dynamics (mechanics)
dynamics (music)
university of the cumberlands
killruddery
southampton, new york
southampton, pennsylvania
southampton, virginia
sarnath