: Mathematics: unitary operator

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unitary operator

In functional analysis, a unitary operator is a surjective bounded operator on a Hilbert space that preserves the inner product. Unitary operators are usually taken as operating on a Hilbert space, but the same notion serves to define the concept of isomorphism between Hilbert spaces.
A unitary element is a generalization of a unitary operator. In a unital algebra, an element $U$ of the algebra is called a unitary element if $U * U = UU * = I$ ,
where $I$ is the identity element.

(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Unitary_operator)

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