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

Abstract

This paper contains the lower and upper bounds of eigenvalues of arrow-head matrices. We propose a parameterized decomposition of the arrowhead matrix which is the 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 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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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2009
Accession Number
ADA593286

Entities

People

  • Bruce W. Suter
  • Lixin Shen

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Air Force
  • Air Force Research Laboratories
  • Communication Systems
  • Eigenvalues
  • Inequalities
  • Interlacing
  • Intervals
  • Mathematical Analysis
  • Mathematics
  • Matrix Theory
  • Multiple Input Multiple Output
  • Numbers
  • Real Numbers
  • Signal Processing
  • Theorems
  • Wireless Communications

Readers

  • Calculus or Mathematical Analysis
  • Coastal and Marine Engineering/Sediment Transport/Hydraulic Engineering