Sign pattern matrices that allow inertia 𝕊n

Abstract

Sign pattern matrices of order n that allow inertias in the set Sn are considered. All sign patterns of order 3 (up to equivalence) that allow S3 are classified and organized according to their associated directed graphs. Furthermore, a minimal set of such matrices is found. Then, given a pattern of order n that allows Sn, a construction is given that generates families of irreducible sign patterns of order n+1 that allow Sn+1.