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In mathematics, the unitary group of degree n
over the field F (which is either the field
R of real numbers or the field C of
complex numbers) 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 numbers then the unitary group coincides with the orthogonal group O(n,R). If F is the
field of complex numbers one usually writes U(n) for the unitary group of degree n.
The unitary group U(n) is a real Lie group of dimension
n2. The Lie algebra of U(n) consists of complex
n-by-n Skew-hermitian matrices, with the Lie bracket given by the commutator.
See also: Special unitary group
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