New Algorithms for Sign k-Potent Sign Patterns

This paper addresses the construction and properties of sign k-potent sign patterns, which are matrices with entries from {+, -, 0} that satisfy a specific power relationship. It improves upon existing algorithms for constructing these patterns, particularly sign idempotent patterns (k=1), by providing a new algorithm that terminates in a single iteration. The paper also provides an algorithm for constructing sign k-potent patterns and conditions for them to allow k-potence. This is important because it provides more efficient and accurate methods for analyzing and constructing these specific types of matrices, which have applications in various fields.