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Eigenvalues, Multiplicities and Graphs

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Title: Eigenvalues, Multiplicities and Graphs
Description: The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than algebraic multiplicities or the numerical values of the eigenvalues. This book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the graph is a tree, work on eigenvalues, multiplicities and graphs has provided the opportunity to identify which ideas have analogs for non-trees, and those for which trees are essential. It gathers and organizes the fundamental ideas to allow students and researchers to easily access and investigate the many interesting questions in the subject.
Authors: Charles R. Johnson, Carlos M. Saiago
Resource Type: eBook.
Subjects: Matrices, Eigenvalues, Symmetric matrices, Trees (Graph theory)
Categories: MATHEMATICS / Discrete Mathematics
Database: eBook Collection (EBSCOhost)
FullText Links:
  – Type: ebook-pdf
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  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 1694366
RelevancyScore: 1084
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1083.55249023438
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Eigenvalues, Multiplicities and Graphs
– Name: Abstract
  Label: Description
  Group: Ab
  Data: The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than algebraic multiplicities or the numerical values of the eigenvalues. This book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the graph is a tree, work on eigenvalues, multiplicities and graphs has provided the opportunity to identify which ideas have analogs for non-trees, and those for which trees are essential. It gathers and organizes the fundamental ideas to allow students and researchers to easily access and investigate the many interesting questions in the subject.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Charles+R%2E+Johnson%22">Charles R. Johnson</searchLink><br /><searchLink fieldCode="AR" term="%22Carlos+M%2E+Saiago%22">Carlos M. Saiago</searchLink>
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  Data: eBook.
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  Data: <searchLink fieldCode="DE" term="%22Matrices%22">Matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetric+matrices%22">Symmetric matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Trees+%28Graph+theory%29%22">Trees (Graph theory)</searchLink>
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  Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Discrete+Mathematics%22">MATHEMATICS / Discrete Mathematics</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 512.9434
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Matrices
        Type: general
      – SubjectFull: Eigenvalues
        Type: general
      – SubjectFull: Symmetric matrices
        Type: general
      – SubjectFull: Trees (Graph theory)
        Type: general
    Titles:
      – TitleFull: Eigenvalues, Multiplicities and Graphs
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Charles R. Johnson
      – PersonEntity:
          Name:
            NameFull: Carlos M. Saiago
      – PersonEntity:
          Name:
            NameFull: Charles R. Johnson
      – PersonEntity:
          Name:
            NameFull: Carlos M. Saiago
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2018
            – D: 08
              M: 03
              Type: profile
              Y: 2018
          Identifiers:
            – Type: isbn-print
              Value: 9781107095458
            – Type: isbn-electronic
              Value: 9781108548137
          Numbering:
            – Type: volume
              Value: 00211
          Titles:
            – TitleFull: Eigenvalues, Multiplicities and Graphs
              Type: main
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