The period and base of a reducible sign pattern matrix Original Research Article

A square sign pattern matrix image (whose entries are image) is said to be powerful if all the powers image are unambiguously defined. For a powerful pattern image, if image with image and image minimal, then image is called the base of image and image is called the period of Li et al. [On the period and base of a sign pattern matrix, Linear Algebra Appl. 212/213 (1994) 101–120] characterized irreducible powerful sign pattern matrices. In this paper, we characterize reducible, powerful sign pattern matrices and give some new results on the period and base of a powerful sign pattern matrix.