The aim of this work is to show the consistency of all systems of non-homogeneous linear difference equations of the form $\phi (x_{n+1})=x_n+v_0$, where $\phi \in {\mathrm{End}}_k(V)$ is a finite potent endomorphism of an arbitrary vector space V and $v_0\in V$. 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.

中文翻译：

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有限自同态非齐次差分方程的显式解

这项工作的目的是显示所有形式的非齐次线性差分方程组的一致性$\phi (X_{n+\mathrm{1个}})=X_n+v_0$， 在哪里$\phi \in {\mathrm{结尾}}_k(V)$是任意向量空间V的有限有效自同态，并且$v_0\in V$. 给出了计算这些系统的解集的算法。特别地，所提供的方法对于计算非齐次差分方程组的显式解是有效的$\mathrm{一种}(X_{n+\mathrm{1个}})=X_n+b$，其中A是有限方阵。