2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63576In this note, firstly we give an easy proof of the factorization of symmetric matrices (see [Mos] math-ph/0203023), then we use it to prove the well-known fact that the automorphism group of a non-degenerate symmetric bilinear form acts transitively on the locus of isotropic subspaces Σ_k.elementary & 4 pagesAlgebraic GeometryRings and Algebrastext