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|Title:||On the Lyapunov and Stein Equations, II|
|Keywords:||Inertia of matrices|
|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.|
|Appears in Collections:||MAT - Artigos|
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