Explicit solutions of non-homogeneous difference equations from finite potent endomorphisms

The aim of this work is to show the consistency of all systems of non-homogeneous linear difference equations of the form , where is a finite potent endomorphism of an arbitrary vector space V and . An algorithm to compute the set of solutions of these systems is given. In particular, the method offered is valid for computing the explicit solutions of the system of non-homogeneous difference equations , with A being a finite square matrix.