Totally nonnegative matrices:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton
Princeton University Press
c2011
|
| Series: | Princeton series in applied mathematics
|
| Subjects: | |
| Online Access: | FAW01 FAW02 Volltext |
| Item 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"-- ""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"-- Includes bibliographical references (p. [219]-238) and index |
| Physical Description: | 1 Online-Ressource (248 p.) |
| ISBN: | 0691121575 1400839017 9780691121574 9781400839018 |
Staff View
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| 500 | |a "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"-- | ||
| 500 | |a ""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"-- | ||
| 500 | |a Includes bibliographical references (p. [219]-238) and index | ||
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Record in the Search Index
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| any_adam_object | |
| author | Fallat, Shaun M. |
| author_facet | Fallat, Shaun M. |
| author_role | aut |
| author_sort | Fallat, Shaun M. |
| author_variant | s m f sm smf |
| building | Verbundindex |
| bvnumber | BV043091932 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)713259161 (DE-599)BVBBV043091932 |
| dewey-full | 512.9/434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/434 |
| dewey-search | 512.9/434 |
| dewey-sort | 3512.9 3434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043091932 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:17:10Z |
| institution | BVB |
| isbn | 0691121575 1400839017 9780691121574 9781400839018 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028516124 |
| oclc_num | 713259161 |
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| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (248 p.) |
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| publishDate | 2011 |
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| publisher | Princeton University Press |
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| series2 | Princeton series in applied mathematics |
| spelling | Fallat, Shaun M. Verfasser aut Totally nonnegative matrices Shaun M. Fallat, Charles R. Johnson Princeton Princeton University Press c2011 1 Online-Ressource (248 p.) txt rdacontent c rdamedia cr rdacarrier Princeton series in applied mathematics "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"-- Includes bibliographical references (p. [219]-238) and index MATHEMATICS / Applied bisacsh MATHEMATICS / Matrices bisacsh MATHEMATICS / Algebra / Linear bisacsh Non-negative matrices local Non-negative matrices fast Non-negative matrices Nichtnegative Matrix (DE-588)4310434-4 gnd rswk-swf Nichtnegative Matrix (DE-588)4310434-4 s 1\p DE-604 Johnson, Charles R. Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=360060 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fallat, Shaun M. Totally nonnegative matrices MATHEMATICS / Applied bisacsh MATHEMATICS / Matrices bisacsh MATHEMATICS / Algebra / Linear bisacsh Non-negative matrices local Non-negative matrices fast Non-negative matrices Nichtnegative Matrix (DE-588)4310434-4 gnd |
| subject_GND | (DE-588)4310434-4 |
| title | Totally nonnegative matrices |
| title_auth | Totally nonnegative matrices |
| title_exact_search | Totally nonnegative matrices |
| title_full | Totally nonnegative matrices Shaun M. Fallat, Charles R. Johnson |
| title_fullStr | Totally nonnegative matrices Shaun M. Fallat, Charles R. Johnson |
| title_full_unstemmed | Totally nonnegative matrices Shaun M. Fallat, Charles R. Johnson |
| title_short | Totally nonnegative matrices |
| title_sort | totally nonnegative matrices |
| topic | MATHEMATICS / Applied bisacsh MATHEMATICS / Matrices bisacsh MATHEMATICS / Algebra / Linear bisacsh Non-negative matrices local Non-negative matrices fast Non-negative matrices Nichtnegative Matrix (DE-588)4310434-4 gnd |
| topic_facet | MATHEMATICS / Applied MATHEMATICS / Matrices MATHEMATICS / Algebra / Linear Non-negative matrices Nichtnegative Matrix |
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