In mathematics, the generalized orthogonal group, O(p, q) is the group of all linear transformations of a p + q dimensional real vector space which leave invariant a nondegenerate, symmetric, bilinear form of signature (p, q) (i.e. the metric has p positive and q negative eigenvalues). Note that O(p, q) is typically defined for vector spaces over the realss since for complex spaces, O(p, q; C) coincides with the normal orthogonal group O(p + q; C).
The generalized special orthogonal group, SO(p, q) is the subgroup of O(p, q) having unit determinant.
See also: Orthogonal group, Lorentz group -- O(1, 3)
