Linear recurrence relations in the algebra of matrices and applications

摘要

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 greater than or equal to r) and e(tA) for every r x r matrix A, in terms of the coefficients of its characteristic polynomial and matrices A(j), where 0 less than or equal to j less than or equal to r - 1. (C) 2001 Elsevier Science Inc. All rights reserved. [References: 16]