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

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 i...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 363; pp. 147 - 159
Main Authors Johnson, Charles R., Leal Duarte, António, Saiago, Carlos M., Sutton, Brian D., Witt, Andrew J.
Format Journal Article Conference Proceeding
LanguageEnglish
Published New York, NY Elsevier Inc 01.04.2003
Elsevier Science
Subjects
Algebra
Eigenvalues
Exact sciences and technology
Hermitian matrix
Linear and multilinear algebra, matrix theory
Mathematics
Multiplicity
Parter vertices
Sciences and techniques of general use
Tree
Vertex degress
Eigenvalues
Hermitian matrix
Vertex degress
Tree
Parter vertices
Multiplicity
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Summary: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(01)00589-4