Open Access Research Article

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

Lixin Shen1 and Bruce W Suter2*

Author Affiliations

1 Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA

2 Air Force Research Laboratory, RITC, Rome, NY 13441-4505, USA

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EURASIP Journal on Advances in Signal Processing 2009, 2009:379402  doi:10.1155/2009/379402

The electronic version of this article is the complete one and can be found online at:

Received: 29 June 2009
Accepted: 15 September 2009
Published: 13 December 2009

© 2009 The Author(s).

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.


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.

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