The space of density states in geometrical quantum mechanics

We 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 $\text{D}(\text{Hil})$ from a geometrical perspective identifying the stratification associated to the natural $GL(\text{Hil})$–action on $\text{D}(\text{Hil})$ and some of its properties. We apply this construction to the cases of quantum systems of two and three levels.