Possible inertia combinations in the Stein and Lyapunov equations
The authors consider the Stein equation \(K - AKA^* = H\) (which arises in the study of discrete-time dynamical systems) and the Lyapunov equation \(KA + A^*K = H\) (which arises in the analysis of continuous- time dynamical systems). For these it is shown that the only joint constraints on the inertias of the three matrices are the classical definiteness and semidefiniteness constraints and a simple rank-related constraint.
scientific article; zbMATH DE number 778242
scientific article