The lattice of faces of a finite dimensional cone

Abstract

In recent years the classical Perron-Frobenius theory has been extended to matrices which leave invariant a cone in the finite dimensional real space V. Here we shall be concerned with the geometry of those cones which are suitable for Perron-Frobenius theory. l Although there is an extensive theory dealing with the lattice of faces of a polyhedral convex set, our work is of a different spirit, especially as parts of it extend to cones which are not polyhedral.