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 M. Saiago; Brian D. Sutton; Andrew J. Witt

doi:10.1016/S0024-3795(01)00589-4

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 M. Saiago
, Brian D. Sutton
, Andrew J. Witt

Department of Computer Science & Engineering

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

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 language	English
Pages (from-to)	147-159
Number of pages	13
Journal	Linear Algebra and Its Applications
Volume	363
DOIs	https://doi.org/10.1016/S0024-3795(01)00589-4
State	Published - Apr 1 2003

Keywords

Eigenvalues
Hermitian matrix
Multiplicity
Parter vertices
Tree
Vertex degress

Access to Document

10.1016/S0024-3795(01)00589-4

Cite this

@article{cb4f5cb8a5db467db8d61c2f4dfb8599,

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

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.",

keywords = "Eigenvalues, Hermitian matrix, Multiplicity, Parter vertices, Tree, Vertex degress",

author = "Johnson, \{Charles R.\} and \{Leal Duarte\}, Ant{\'o}nio and Saiago, \{Carlos M.\} and Sutton, \{Brian D.\} and Witt, \{Andrew J.\}",

year = "2003",

month = apr,

day = "1",

doi = "10.1016/S0024-3795(01)00589-4",

language = "English",

volume = "363",

pages = "147--159",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

}

TY - JOUR

T1 - On the relative position of multiple eigenvalues in the spectrum of an Hermitian matrix with a given graph

AU - Johnson, Charles R.

AU - Leal Duarte, António

AU - Saiago, Carlos M.

AU - Sutton, Brian D.

AU - Witt, Andrew J.

PY - 2003/4/1

Y1 - 2003/4/1

N2 - 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.

AB - 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.

KW - Eigenvalues

KW - Hermitian matrix

KW - Multiplicity

KW - Parter vertices

KW - Tree

KW - Vertex degress

UR - https://www.scopus.com/pages/publications/84867974280

U2 - 10.1016/S0024-3795(01)00589-4

DO - 10.1016/S0024-3795(01)00589-4

M3 - Article

AN - SCOPUS:84867974280

SN - 0024-3795

VL - 363

SP - 147

EP - 159

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this