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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 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.
See also:
- Category:Unitary operators
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