On the relative position of multiple eigenvalues in the spectrum of an Hermitian matrix with a given graph

Charles R. Johnson, António Leal-Duarte, Carlos Manuel Saiago, Brian D. Sutton, Andrew J. Witt

Research output: Contribution to journalConference article

32 Citations (Scopus)
6 Downloads (Pure)

Abstract

For Hermitian matrices, whose graph is a given tree, the relationships among vertex degrees, multiple eigenvalues and the relative position of the underlying eigenvalue in the ordered spectrum are discussed in detail. In the process, certain aspects of special vertices, whose removal results in an increase in multiplicity are investigated.
Original languageEnglish
Pages (from-to)147-159
Number of pages13
JournalLinear Algebra and Its Applications
Volume363
DOIs
Publication statusPublished - 1 Apr 2003
EventWorkshop on Nonnegative Matrices, M-matrices and Generalizations - Oberwolfach, Germany
Duration: 26 Nov 20002 Dec 2000

Keywords

  • Eigenvalues
  • Hermitian matrix
  • Multiplicity
  • Parter vertices
  • Tree
  • Vertex degrees

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