Reducible pattern k-potent ray pattern matrices Original Research Article

A ray pattern A is called pattern k-potent if k is the smallest positive integer such that Ak+1=A as ray patterns. The structure of irreducible, pattern k-potent ray patterns was characterized by Stuart, Beasley and Shader. 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, pattern k-potent ray pattern.