ON THE PERIOD AND BASE OF A SIGN PATTERN MATRIX

A square sign pattern matrix A (whose entries are +, -, or 0) is said to be powerful if all the powers A(1), A(2), A(3),..., are unambiguously defined. For a powerful pattern A, if A(l) = A(l+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.