Totally positive matrices:
"Totally positive matrices constitute a particular class of matrices, the study of which was initiated by analysts because of its many applications in diverse areas. This modern account of the subject is comprehensive and thorough, with careful treatment of the central properties of totally pos...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge tracts in mathematics
181 |
| Schlagworte: | |
| Online-Zugang: | Cover image Inhaltsverzeichnis |
| Zusammenfassung: | "Totally positive matrices constitute a particular class of matrices, the study of which was initiated by analysts because of its many applications in diverse areas. This modern account of the subject is comprehensive and thorough, with careful treatment of the central properties of totally positive matrices, full proofs and a complete bibliography. The history of the subject is also described: in particular, the book ends with a tribute to the four people who have made the most notable contributions to the history of total positivity: I. J. Schoenberg, M. G. Krein, F. R. Gantmacher and S. Karlin. This monograph will appeal to those with an interest in matrix theory, to those who use or have used total positivity, and to anyone who wishes to learn about this rich and interesting subject"--Provided by publisher. |
| Beschreibung: | XI, 181 S. Ill. |
| ISBN: | 9780521194082 |
Internformat
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| 245 | 1 | 0 | |a Totally positive matrices |c Allan Pinkus |
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| 300 | |a XI, 181 S. |b Ill. | ||
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| 490 | 1 | |a Cambridge tracts in mathematics |v 181 | |
| 520 | 3 | |a "Totally positive matrices constitute a particular class of matrices, the study of which was initiated by analysts because of its many applications in diverse areas. This modern account of the subject is comprehensive and thorough, with careful treatment of the central properties of totally positive matrices, full proofs and a complete bibliography. The history of the subject is also described: in particular, the book ends with a tribute to the four people who have made the most notable contributions to the history of total positivity: I. J. Schoenberg, M. G. Krein, F. R. Gantmacher and S. Karlin. This monograph will appeal to those with an interest in matrix theory, to those who use or have used total positivity, and to anyone who wishes to learn about this rich and interesting subject"--Provided by publisher. | |
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| 650 | 0 | 7 | |a Positive Matrix |0 (DE-588)7696958-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804140852175437824 |
|---|---|
| adam_text | Titel: Totally positive matrices
Autor: Pinkus, Allan
Jahr: 2010
Contents
Foreword page ix
1 Basic properties of totally positive and strictly
totally positive matrices 1
1.1 Preliminaries 1
1.2 Building (strictly) totally positive matrices 5
1.3 Nonsingularity and rank 12
1.4 Determinantal inequalities 24
1.5 Remarks 33
2 Criteria for total positivity and strict total
positivity 36
2.1 Criteria for strict total positivity 37
2.2 Density and some further applications 41
2.3 Triangular total positivity 47
2.4 LDU factorizations 50
2.5 Criteria for total positivity 55
2.6 Simple criteria for strict total positivity 60
2.7 Remarks 74
3 Variation diminishing 76
3.1 Main equivalence theorems 76
3.2 Intervals of strict total positivity 83
3.3 Remarks 85
4 Examples 87
4.1 Totally positive kernels and Descartes systems 87
4.2 Exponentials and powers 88
4.3 Cauchy matrix 92
4.4 Green s matrices 94
4.5 Jacobi matrices 97
Contents
4.6 Hankel matrices 101
4.7 Toeplitz matrices 104
4.8 Generalized Hurwitz matrices 111
4.9 More on Toeplitz matrices 117
4.10 Hadamard products of totally positive matrices 119
4.11 Remarks 125
5 Eigenvalues and eigenvectors 127
5.1 Oscillation matrices 127
5.2 The Gantmacher-Krein theorem 130
5.3 Eigenvalues of principal submatrices 140
5.4 Eigenvectors 144
5.5 Eigenvalues as functions of matrix elements 149
5.6 Remarks 152
6 Factorizations of totally positive matrices 154
6.1 Preliminaries 154
6.2 Factorizations of strictly totally positive matrices 156
6.3 Factorizations of totally positive matrices 164
6.4 Remarks 167
Afterword 169
References 174
Author index 180
Subject index 182
|
| any_adam_object | 1 |
| author | Pinkus, Allan 1946- |
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| classification_rvk | SK 220 |
| ctrlnum | (OCoLC)444107065 (DE-599)BVBBV035875499 |
| 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 |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV035875499 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:06:33Z |
| institution | BVB |
| isbn | 9780521194082 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018733187 |
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| owner_facet | DE-19 DE-BY-UBM DE-20 DE-83 DE-824 |
| physical | XI, 181 S. Ill. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Pinkus, Allan 1946- Verfasser (DE-588)110369297 aut Totally positive matrices Allan Pinkus 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2010 XI, 181 S. Ill. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 181 "Totally positive matrices constitute a particular class of matrices, the study of which was initiated by analysts because of its many applications in diverse areas. This modern account of the subject is comprehensive and thorough, with careful treatment of the central properties of totally positive matrices, full proofs and a complete bibliography. The history of the subject is also described: in particular, the book ends with a tribute to the four people who have made the most notable contributions to the history of total positivity: I. J. Schoenberg, M. G. Krein, F. R. Gantmacher and S. Karlin. This monograph will appeal to those with an interest in matrix theory, to those who use or have used total positivity, and to anyone who wishes to learn about this rich and interesting subject"--Provided by publisher. Matrices Positive Matrix (DE-588)7696958-7 gnd rswk-swf Positive Matrix (DE-588)7696958-7 s DE-604 Cambridge tracts in mathematics 181 (DE-604)BV000000001 181 http://assets.cambridge.org/97805211/94082/cover/9780521194082.jpg Cover image HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018733187&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pinkus, Allan 1946- Totally positive matrices Cambridge tracts in mathematics Matrices Positive Matrix (DE-588)7696958-7 gnd |
| subject_GND | (DE-588)7696958-7 |
| title | Totally positive matrices |
| title_auth | Totally positive matrices |
| title_exact_search | Totally positive matrices |
| title_full | Totally positive matrices Allan Pinkus |
| title_fullStr | Totally positive matrices Allan Pinkus |
| title_full_unstemmed | Totally positive matrices Allan Pinkus |
| title_short | Totally positive matrices |
| title_sort | totally positive matrices |
| topic | Matrices Positive Matrix (DE-588)7696958-7 gnd |
| topic_facet | Matrices Positive Matrix |
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