# Generalized special orthogonal group

In

mathematics, a

**generalized special orthogonal group**, SO(p,q) is the

group of all linear transformations of a p+q dimensional

real vector space (for

complex vector spaces, there is no difference between SO(p,q) and SO(p+q)) which leave invariant a symmetric 2-

tensor with p positive and q negative eigenvalues.

See also Special orthogonal group.