Symmetric sign pattern matrices that require unique inertia Original Research Article

A sign pattern matrix is a matrix whose entries are from the set {+,−,0}. The purpose of this paper is to characterize symmetric sign patterns that require unique inertia, that is, all the real symmetric matrices with the given sign pattern must have the same inertia. Further, some constructions to obtain sign patterns that require unique inertia are provided. Sign patterns corresponding to some special graphs are also considered. Finally, extensions to complex sign patterns are mentioned.