Reducible sign k-potent sign pattern matrices Original Research Article

The sign pattern matrix A is called sign k-potent if k is the smallest positive integer such that Ak+1=A. The structure of irreducible, sign k-potent pattern matrices was characterized by Stuart et al. (J. Stuart, C. Eschenbach, S. Kirkland, Linear Algebra Appl. 294 (1999) 85–92). We extend those results to the reducible case, providing necessary conditions that characterize the structure of each off-diagonal block of the Frobenius normal form of a reducible, sign k-potent matrix.