Irreducible, pattern k-potent ray pattern matrices Original Research Article

A ray pattern is the class of all complex matrices with a specified zero–nonzero pattern such that the argument of each nonzero entry is specified. The ray pattern A is called pattern k-potent if k is the smallest positive integer for which Ak+1=A as ray patterns. We characterize the irreducible ray patterns that are pattern k-potent, and we provide a canonical form for patterns with respect to permutation similarity and signature similarity by diagonal, unitary matrices.