Acyclic matrices with a small number of distinct eigenvalues

Reshmi Nair, Bryan L. Shader

Research output: Contribution to journalArticle

Abstract

Spectral properties of the set of all symmetric matrices whose graph is a given tree T are further studied. A new technique based on Smith Normal Form and Hamming Distance is introduced and used to characterize such matrices that have at most four distinct eigenvalues and such matrices that have at most two multiple eigenvalues and whose sum of multiplicities is the maximum possible.

Original languageEnglish (US)
Pages (from-to)4075-4089
Number of pages15
JournalLinear Algebra and Its Applications
Volume438
Issue number10
DOIs
StatePublished - May 15 2013
Externally publishedYes

Keywords

  • Acyclic matrix
  • Diameter
  • Hamming distance
  • Maximum multiplicity
  • Smith normal form

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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