# Unitary group

In

abstract algebra, the

**unitary group** of degree

*n* over a

field *F* (written as U(

*n*,

*F*)) is the

group of

*n* by

*n* unitary matrices with entries from

*F*, with the group operation that of

matrix multiplication. This is a

subgroup of the

general linear group Gl(

*n*,

*F*).

If the field *F* is the field of real or complex numbers, then the **unitary group** U(*n*,*F*) is a Lie group.