TY: JOUR
T1 - On the Lyapunov and Stein equations
A1 - Silva, Fernando
A1 - Simões, Rita
N2 - Let L ? Cn × n and let H, K ? Cn × n be Hermitian matrices. The general inertia theorem gives a complete set of relations between the similarity class of L and the congruence class of H, when the Lyapunov equation LH + HL* = K is satisfied and K > 0. In this paper, we give some relations between the similarity class of L and the congruence class of K, when the Lyapunov equation is satisfied and H > 0. We also consider the corresponding problem with the Stein equation. © 2006 Elsevier Inc. All rights reserved.
UR - https://ria.ua.pt/handle/10773/5472
Y1 - 2007
PB - No publisher defined