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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.