Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/8432
Title: | On the Lyapunov and Stein Equations, II |
Author: | Silva, F.C. Simões, R. |
Keywords: | Inertia of matrices Lyapunov equation Stein equation |
Issue Date: | 2007 |
Publisher: | Elsevier |
Abstract: | Let L ∈ Cn × n and let H, K ∈ Cn × n be Hermitian matrices. Some already known results, including the general inertia theorem, give partial answers to the following problem: find a complete set of relations between the similarity class of L and the congruence classes of H and K, when the Lyapunov equation LH + HL* = K is satisfied. In this paper, we solve this problem when L is nonderogatory, H is nonsingular and K has at least one eigenvalue with positive real part and one eigenvalue with negative real part. Our result generalizes a previous paper by L. M. DeAlba. The corresponding problem with the Stein equation follows easily using a Cayley transform. © 2007 Elsevier Inc. All rights reserved. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/8432 |
DOI: | 10.1016/j.laa.2007.05.001 |
ISSN: | 0024-3795 |
Appears in Collections: | DMat - Artigos |
Files in This Item:
File | Description | Size | Format | |
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LAA#0701-018B,RFP#7240R.pdf | 148.02 kB | Adobe PDF | View/Open |
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