Matrix decomposition in products of two involutions. The Wonenburger-Hoffman-Paige Theorem

Over a field of characteristic different from $2$, the Cartan--Dieudonné theorem expresses each orthogonal transformation of a finite dimensional space with a nondegenerate symmetric bilinear form as a product of at most V reflections. When the form has index $0$, Wonenburger proved that two orthogonal involutions suffice. For finite dimensional spaces over fields of characteristic different from $2$, she showed that an invertible transformation A is a product of two involutions exactly when A~ A⁻¹. Hoffman and Paige proved this criterion over arbitrary fields when the space has dimension greater than one.