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The Resource Totally nonnegative matrices, Shaun M. Fallat, Charles R. Johnson, (electronic resource)

Totally nonnegative matrices, Shaun M. Fallat, Charles R. Johnson, (electronic resource)

Label
Totally nonnegative matrices
Title
Totally nonnegative matrices
Statement of responsibility
Shaun M. Fallat, Charles R. Johnson
Creator
Contributor
Subject
Language
eng
Summary
  • "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"--
  • "Totally Nonnegative Matrices" is a comprehensive, modern treatment of the titled class of matrices that arise in very many ways. Methodological background is given, and elementary bidiagonal factorization is a featured tool. In addition to historical highlights and sources of interest, some of the major topics include: recognition, variation diminution, spectral structure, determinantal inequalities, Hadamard products, and completion problems. "--
  • "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"--
  • "Totally Nonnegative Matrices" is a comprehensive, modern treatment of the titled class of matrices that arise in very many ways. Methodological background is given, and elementary bidiagonal factorization is a featured tool. In addition to historical highlights and sources of interest, some of the major topics include: recognition, variation diminution, spectral structure, determinantal inequalities, Hadamard products, and completion problems. "--
  • "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"--
  • "Totally Nonnegative Matrices" is a comprehensive, modern treatment of the titled class of matrices that arise in very many ways. Methodological background is given, and elementary bidiagonal factorization is a featured tool. In addition to historical highlights and sources of interest, some of the major topics include: recognition, variation diminution, spectral structure, determinantal inequalities, Hadamard products, and completion problems. "--
  • "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"--
  • "Totally Nonnegative Matrices" is a comprehensive, modern treatment of the titled class of matrices that arise in very many ways. Methodological background is given, and elementary bidiagonal factorization is a featured tool. In addition to historical highlights and sources of interest, some of the major topics include: recognition, variation diminution, spectral structure, determinantal inequalities, Hadamard products, and completion problems."--
Assigning source
  • Provided by publisher
  • Provided by publisher
  • Provided by publisher
  • Provided by publisher
  • Provided by publisher
  • Provided by publisher
  • Provided by publisher
  • Provided by publisher
Cataloging source
DLC
http://library.link/vocab/creatorName
Fallat, Shaun M
Dewey number
512.9/434
LC call number
QA188
LC item number
.F35 2011
http://library.link/vocab/relatedWorkOrContributorName
Johnson, Charles R
Series statement
Princeton series in applied mathematics
http://library.link/vocab/subjectName
  • Non-negative matrices
  • MATHEMATICS / Applied
  • MATHEMATICS / Matrices
  • MATHEMATICS / Algebra / Linear
Label
Totally nonnegative matrices, Shaun M. Fallat, Charles R. Johnson, (electronic resource)
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. [218]-238) and index
Control code
OCM1bookssj0000473874
Dimensions
unknown
Isbn
9780691121574
Isbn Type
(hardback)
Lccn
2010052042
Specific material designation
remote
System control number
(WaSeSS)bookssj0000473874
Label
Totally nonnegative matrices, Shaun M. Fallat, Charles R. Johnson, (electronic resource)
Publication
Bibliography note
Includes bibliographical references (p. [218]-238) and index
Control code
OCM1bookssj0000473874
Dimensions
unknown
Isbn
9780691121574
Isbn Type
(hardback)
Lccn
2010052042
Specific material designation
remote
System control number
(WaSeSS)bookssj0000473874

Library Locations

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      1 University Blvd, St. Louis, MO, 63121, US
      38.710138 -90.311107
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