2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135015We present a geometrical description of the space of density states of a quantum system of finite dimension. After presenting a brief summary of the geometrical formulation of Quantum Mechanics, we proceed to describe the space of density states $\D(\Hil)$ from a geometrical perspective identifying the stratification associated to the natural $GL(\Hil)$--action on $\D(\Hil)$ and some of its properties. We apply this construction to the cases of quantum systems of two and three levels.Amslatex, 18 pages, 4 figuresQuantum Physicstext