Critical sets of refined inertias for irreducible zero–nonzero patterns of orders 2 and 3

The concept of a critical set of refined inertias for an irreducible zero–nonzero pattern is defined, and all minimal critical sets of refined inertias for irreducible zero–nonzero patterns of orders 2 and 3 are identified. As an application of these results, a new method is used to identify all minimal critical sets of inertias for irreducible zero–nonzero patterns of orders 2 and 3.