Linear recurrence relations in the algebra of matrices and applications Original Research Article

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 An (ngreater-or-equal, slantedr) and etA for every r×r matrix A, in terms of the coefficients of its characteristic polynomial and matrices Aj, where 0less-than-or-equals, slantjless-than-or-equals, slantr−1.