The generation of all rational orthogonal matrices in Rp,q

A method for generating all rational generalized matrices on indefinite real inner product spaces isomorphic to Rp,qRp,q is presented. The proposed method is based on the proof of a weak version of the Cartan–Dieudonné theorem, handled using Clifford algebras. It is shown that all rational BB-orthogonal matrices in an indefinite inner product space (X,B)(X,B) are products of simple matrices with rational entries.