On the period and base of a sign pattern matrix

Abstract

AbstractA square sign pattern matrix A (whose entries are +, −, or 0) is said to be powerful if all the powers A1, A2, A3,…, are unambiguously defined. For a powerful pattern A, if Al=Al+p with l and p minimal, then l is called the base of A and p is called the period of A. We characterize irreducible powerful sign pattern matrices and investigate the period and base of a powerful sign pattern matrix. We also consider some connections with real matrices and give some significant classes of powerful patterns