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Possible inertia combinations in the Stein and Lyapunov equations

✍ Scribed by Luz M. DeAlba; Charles R. Johnson

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
830 KB
Volume
222
Category
Article
ISSN
0024-3795

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Let L ∈ C nΓ—n and let H, K ∈ C nΓ—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 th

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A be an n X n complex matrix with inertia In(A) = (r(A), a(A), s(A)), and let H be an n x n hermitian matrix with inertia In(H) = (r(H), 6(H), 6(H)). Let K b e an n X n positive semidefinite matrix such that K = AH + HA\*. Suppose that 1 is the dimension of the controllability space of the pair (A,