The general unitary group is the subgroup of all elements of the general linear group that fix a given nonsingular Hermitian form. This is equivalent, in the canonical case, to the definition of as the group of unitary matrices.
General Unitary Group
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ReferencesConway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. "The Groups , , , and ." §2.2 in Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, p. x, 1985.
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Weisstein, Eric W. "General Unitary Group." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GeneralUnitaryGroup.html