TY - BOOK UR - http://lib.ugent.be/catalog/ebk01:2670000000081283 ID - ebk01:2670000000081283 ET - Course Book. LA - eng TI - Totally Nonnegative Matrices PY - 2011 SN - 9781400839018 AU - Fallat, Shaun M., author. AU - Johnson, Charles R., author. AB - 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. ER -Download RIS file
05426nam a2200829 i 4500 | |||
001 | 9781400839018 | ||
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020 | a 9781400839018 | ||
024 | 7 | a 10.1515/9781400839018 2 doi | |
035 | a (DE-B1597)447017 | ||
035 | a (OCoLC)713259161 | ||
040 | a IN-ChSCO b eng c IN-ChSCO e rda | ||
041 | a eng | ||
050 | 4 | a QA188 | |
050 | 4 | a QA188 b .F35 2011eb | |
072 | 7 | a MAT x 003000 2 bisacsh | |
072 | 7 | a MAT003000 2 bisacsh | |
082 | 4 | a 512.9/434 2 22 | |
082 | 4 | a 512.9/434 2 23 | |
100 | 1 | a Fallat, Shaun M., e author. | |
245 | 1 | a Totally Nonnegative Matrices / c Shaun M. Fallat, Charles R. Johnson. | |
250 | a Course Book. | ||
264 | 1 | a Princeton, N.J. : b Princeton University Press, c [2011]. | |
264 | 4 | c Â©2011. | |
300 | a 1 online resource (264 pages) : b illustrations. | ||
336 | a text 2 rdacontent | ||
337 | a computer 2 rdamedia | ||
338 | a online resource 2 rdacarrier | ||
347 | a text file b PDF 2 rda | ||
490 | a Princeton Series in Applied Mathematics | ||
505 | t Frontmatter -- t Contents -- t List of Figures -- t Preface -- t Chapter 0. Introduction -- t Chapter One. Preliminary Results and Discussion -- t Chapter Two. Bidiagonal Factorization -- t Chapter Three. Recognition -- t Chapter Four. Sign Variation of Vectors and TN Linear Transformations -- t Chapter Five. The Spectral Structure of TN Matrices -- t Chapter Six. Determinantal Inequalities for TN Matrices -- t Chapter Seven. Row and Column Inclusion and the Distribution of Rank -- t Chapter Eight. Hadamard Products and Powers of TN Matrices -- t Chapter Nine. Extensions and Completions -- t Chapter Ten. Other Related Topics on TN Matrices -- t Bibliography -- t List of Symbols -- t Index. | ||
520 | 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. | ||
533 | a Electronic reproduction. b Princeton, N.J. : c Princeton University Press, d 2011. n Mode of access: World Wide Web. n System requirements: Web browser. n Access may be restricted to users at subscribing institutions. | ||
538 | a Mode of access: Internet via World Wide Web. | ||
546 | a In English. | ||
588 | a Description based on online resource; title from PDF title page (publisherâ€™s Web site, viewed October 27 2015) | ||
650 | a MATHEMATICS v Algebra v Linear. | ||
650 | a MATHEMATICS v Applied. | ||
650 | a MATHEMATICS v Matrices. | ||
650 | a Non-negative matrices. | ||
650 | 4 | a Applied Mathematics. | |
650 | 4 | a Mathematics. | |
650 | 4 | a Mathematik. | |
650 | 4 | a Non-negative matrices. | |
650 | 7 | a MATHEMATICS x Applied. 2 bisacsh. | |
700 | 1 | a Johnson, Charles R., e author. | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton eBook Package Backlist 2000-2013 z 978-3-11-044250-2 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton eBook Package Backlist 2000-2014 z 978-3-11-045953-1 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton Series in Applied Mathematics ebook package z 978-3-11-051583-1 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton Univ. Press eBook Package 2000-2013 z 978-3-11-041343-4 | |
830 | a Princeton Series in Applied Mathematics. | ||
856 | 4 | u https://doi.org/10.1515/9781400839018 | |
856 | 4 | 2 | 3 Cover u https://www.degruyter.com/doc/cover/9781400839018.jpg |
912 | a 978-3-11-041343-4 Princeton Univ. Press eBook Package 2000-2013 | ||
912 | a 978-3-11-044250-2 Princeton eBook Package Backlist 2000-2013 | ||
912 | a 978-3-11-045953-1 Princeton eBook Package Backlist 2000-2014 | ||
912 | a 978-3-11-051583-1 Princeton Series in Applied Mathematics ebook package | ||
912 | a GBV-deGruyter-alles | ||
912 | a GBV-deGruyter-PDA12STME | ||
912 | a GBV-deGruyter-PDA13ENGE | ||
912 | a GBV-deGruyter-PDA14ALL | ||
912 | a GBV-deGruyter-PDA15STM | ||
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912 | a GBV-deGruyter-PDA5EBK | ||
912 | a GBV-deGruyter-PDA7ENG | ||
912 | a GBV-deGruyter-PDA9PRIN |
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