Linear recurrence relations in the algebra of matrices and applications

Abstract

We study here some linear recurrence relations in the algebra of square matrices. With the aid of the Cayley–Hamilton Theorem, we derive some explicit formulas for A n (n⩾r) and e tA for every r×r matrix A, in terms of the coefficients of its characteristic polynomial and matrices A j , where 0⩽j⩽r−1.