Irreducible sign \(k\)-potent sign pattern matrices
A matrix whose entries are from the set \(\{ +, -, 0 \}\) is called a sign pattern matrix. A square sign pattern matrix \(A\) is called sign \(k\)-potent if \(k\) is the smallest positive integer for which \(A^{k+1} = A\) holds. (In the case \(k = 1\), \(A\) is called sign idempotent.) The authors not only present a full characterization of those irreducible sign pattern matrices that are sign \(k\)-potent but also provide canonical forms for such matrices.
scientific article; zbMATH DE number 1371393