A characterization of convex cones of matrices with constant regular inertia (Q1590643)

A necessary and sufficient condition is found for a convex cone of complex \(n\times n\) matrices to contain matrices with constant regular inertia. This condition is of the form \(\text{Re} (x^*HAx)>0\) for every non-zero vector \(x\) and a Hermitian matrix. The procedure uses the extreme point method and is based on a version of the Lyapunov equation. The work is an extension of a previous paper of the authors [ibid. 250, 105-131 (1997; Zbl 0871.15012)].