The general orthogonal group 
is the subgroup of all
elements of the projective general linear
group that fix the particular nonsingular quadratic
form 
.
The determinant of such an element is 
.
General Orthogonal Group
See also
Projective General Linear GroupExplore with Wolfram|Alpha
References
Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. "The Groups
, 
, 
, and 
, and 
." §2.4 in Atlas
of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups.
Oxford, England: Clarendon Press, pp. xi-xii, 1985.Referenced on Wolfram|Alpha
General Orthogonal GroupCite this as:
Weisstein, Eric W. "General Orthogonal Group." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GeneralOrthogonalGroup.html