Definition:Unitary Group

Definition
Let $n$ be a positive integer.

The unitary group $\operatorname{U}_n$ is the group of all $n\times n$ unitary matrices.

Unitary Group of Hilbert Space
Let $H$ be a Hilbert space.

Its unitary group is the group consisting of its unitary operators.

Also see

 * Definition:Orthogonal Group
 * Definition:Special Unitary Group