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  • Research Article
  • Open Access

Bounds for Eigenvalues of Arrowhead Matrices and Their Applications to Hub Matrices and Wireless Communications

EURASIP Journal on Advances in Signal Processing20092009:379402

https://doi.org/10.1155/2009/379402

  • Received: 29 June 2009
  • Accepted: 15 September 2009
  • Published:

Abstract

This paper considers the lower and upper bounds of eigenvalues of arrow-head matrices. We propose a parameterized decomposition of an arrowhead matrix which is a sum of a diagonal matrix and a special kind of arrowhead matrix whose eigenvalues can be computed explicitly. The eigenvalues of the arrowhead matrix are then estimated in terms of eigenvalues of the diagonal matrix and the special arrowhead matrix by using Weyl's theorem. Improved bounds of the eigenvalues are obtained by choosing a decomposition of the arrowhead matrix which can provide best bounds. Some applications of these results to hub matrices and wireless communications are discussed.

Keywords

  • Information Technology
  • Diagonal Matrix
  • Wireless Communication
  • Quantum Information
  • Special Kind

Publisher note

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Authors’ Affiliations

(1)
Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA
(2)
Air Force Research Laboratory, RITC, Rome, NY 13441-4505, USA

Copyright

© L. Shen and B.W. Suter. 2009

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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