Editing Unitary operator (section)

{{short description|Surjective bounded operator on a Hilbert space preserving the inner product}}
{{distinguish|Unitarity (physics)}}

In [[functional analysis]], a '''unitary operator''' is a [[surjective function|surjective]] [[bounded operator]] on a [[Hilbert space]] that preserves the [[inner product]].
Non-trivial examples include rotations,  reflections, and the [[Fourier operator]].
Unitary operators generalize [[unitary matrix|unitary matrices]].
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.