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

Abstract

[EN] The aim of this work is to show the consistency of all systems of nonhomogeneous linear difference equations of the form ϕ(x_n+1) = x_n + v_0, where ϕ ∈ End_k(V) is a finite potent endomorphism of an arbitrary vector space V and v_0 ∈ V. 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 A(x_n+1) = x_n + b, with A being a finite square matrix.