Algorithms for solving the inverse problem associated with KAK=As+1KAK=As+1

In previous papers, the authors introduced and characterized a class of matrices called {K,s+1}{K,s+1}-potent. Also, they established a method to construct these matrices. The purpose of this paper is to solve the associated inverse problem. Several algorithms are developed in order to find all involutory matrices KK satisfying KAs+1K=AKAs+1K=A for a given matrix A∈Cn×nA∈Cn×n and a given natural number ss. The cases s=0s=0 and s≥1s≥1 are separately studied since they produce different situations. In addition, some examples are presented showing the numerical performance of the methods.