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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An application of the separation theorem for hermitian matrices


Author: T. L. Markham
Journal: Proc. Amer. Math. Soc. 47 (1975), 61-64
MSC: Primary 15A18
MathSciNet review: 0364290
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Abstract: Suppose $ H$ is an $ n \times n$ hermitian matrix over the complex field partitioned as $ H = \left(\begin{smallmatrix}A&B\\ B*&C\end{smallmatrix}\right)$, where $ C$ is invertible. Using the separation theorem on eigenvalues of hermitian matrices, bounds are obtained for the eigenvalues of $ (H/C) = A - B{C^{ - 1}}{B^ \ast }$ in terms of the eigenvalues of $ H$ and $ C$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0364290-1
PII: S 0002-9939(1975)0364290-1
Keywords: Separation theorem, hermitian matrices, Schur complement, compound matrix, bounds for eigenvalues
Article copyright: © Copyright 1975 American Mathematical Society