Basis partition of the space of linear programs through a differential equation

The space of linear programs (LP) can be partitioned into a finite number of sets, each corresponding to a basis. This partition is thus called the basis partition. The closed-form solution on the space of LP can be determined with the basis partition if we can characterize the basis partition. A differential equation on the Grassmann manifold which represents the space of LP provides a powerful tool for characterizing the basis partition. In paper [3], the author presented some basic concepts and properties of this differential equation. This paper continues the research of [3] and presents three useful properties.