On the inertia of the Lyapunov transform AH + HA * for H >0
Sara Avraham, Raphael Loewy · Linear and Multilinear Algebra · 1978
Given an arbitrary n×n matrix A with complex entries, we characterize all inertia triples (a b c) that are attained by the Lyapunov transform AH+ HA *, as H varies over the set of all n× n positive definite matrices.