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.
Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A.
``The Groups , ,
.'' §2.2 in
Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England:
Clarendon Press, p. x, 1985.