文摘
In previous papers, the authors introduced and characterized a class of matrices called 88a451cffd683d7f" title="Click to view the MathML source">{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 bdd47ccf594b9f4" title="Click to view the MathML source">K satisfying 8889425548288cad9" title="Click to view the MathML source">KAs+1K=A for a given matrix A∈Cn×n and a given natural number bd3da22279abc8c7c86" title="Click to view the MathML source">s. The cases a2fc733ae6db" title="Click to view the MathML source">s=0 and e50bbc4ffe7862b1715ff59dbd36" title="Click to view the MathML source">s≥1 are separately studied since they produce different situations. In addition, some examples are presented showing the numerical performance of the methods.