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Totally Nonnegative Matrices

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Title: Totally Nonnegative Matrices
Description: Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, historical highlights of key ideas, and specialized topics.The book uses classical and ad hoc tools, but a unifying theme is the elementary bidiagonal factorization, which has emerged as the single most important tool for this particular class of matrices. Recent work has shown that bidiagonal factorizations may be viewed in a succinct combinatorial way, leading to many deep insights. Despite slow development, bidiagonal factorizations, along with determinants, now provide the dominant methodology for understanding total nonnegativity. The remainder of the book treats important topics, such as recognition of totally nonnegative or totally positive matrices, variation diminution, spectral properties, determinantal inequalities, Hadamard products, and completion problems associated with totally nonnegative or totally positive matrices. The book also contains sample applications, an up-to-date bibliography, a glossary of all symbols used, an index, and related references.
Authors: Shaun M. Fallat, Charles R. Johnson
Resource Type: eBook.
Subjects: Non-negative matrices
Categories: MATHEMATICS / Applied, MATHEMATICS / Algebra / Linear, MATHEMATICS / Matrices
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-epub
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Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 360060
RelevancyScore: 1038
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1037.72192382813
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  Data: Totally Nonnegative Matrices
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  Data: Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, historical highlights of key ideas, and specialized topics.The book uses classical and ad hoc tools, but a unifying theme is the elementary bidiagonal factorization, which has emerged as the single most important tool for this particular class of matrices. Recent work has shown that bidiagonal factorizations may be viewed in a succinct combinatorial way, leading to many deep insights. Despite slow development, bidiagonal factorizations, along with determinants, now provide the dominant methodology for understanding total nonnegativity. The remainder of the book treats important topics, such as recognition of totally nonnegative or totally positive matrices, variation diminution, spectral properties, determinantal inequalities, Hadamard products, and completion problems associated with totally nonnegative or totally positive matrices. The book also contains sample applications, an up-to-date bibliography, a glossary of all symbols used, an index, and related references.
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  Data: <searchLink fieldCode="AR" term="%22Shaun+M%2E+Fallat%22">Shaun M. Fallat</searchLink><br /><searchLink fieldCode="AR" term="%22Charles+R%2E+Johnson%22">Charles R. Johnson</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 512.9434
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Non-negative matrices
        Type: general
    Titles:
      – TitleFull: Totally Nonnegative Matrices
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Shaun M. Fallat
      – PersonEntity:
          Name:
            NameFull: Charles R. Johnson
      – PersonEntity:
          Name:
            NameFull: Shaun M. Fallat
      – PersonEntity:
          Name:
            NameFull: Charles R. Johnson
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2011
            – D: 04
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9780691121574
            – Type: isbn-print
              Value: 9780691242415
            – Type: isbn-electronic
              Value: 9781400839018
          Titles:
            – TitleFull: Totally Nonnegative Matrices
              Type: main
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