Positive definite matrices:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ [u.a]
Princeton Univ. Press
2007
|
| Schriftenreihe: | Princeton series in applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | IX, 254 S. graph. Darst. |
| ISBN: | 9780691129181 0691129185 9780691168258 |
Internformat
MARC
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| 100 | 1 | |a Bhatia, Rajendra |d 1952- |e Verfasser |0 (DE-588)104344431 |4 aut | |
| 245 | 1 | 0 | |a Positive definite matrices |c Rajendra Bhatia |
| 264 | 1 | |a Princeton, NJ [u.a] |b Princeton Univ. Press |c 2007 | |
| 300 | |a IX, 254 S. |b graph. Darst. | ||
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| 490 | 0 | |a Princeton series in applied mathematics | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface vii
Chapter 1. Positive Matrices 1
1.1 Characterizations 1
1.2 Some Basic Theorems 5
1.3 Block Matrices 12
1.4 Norm of the Schur Product 16
1.5 Monotonicity and Convexity 18
1.6 Supplementary Results and Exercises 23
1.7 Notes and References 29
Chapter 2. Positive Linear Maps 35
2.1 Representations 35
2.2 Positive Maps 36
2.3 Some Basic Properties of Positive Maps 38
2.4 Some Applications 43
2.5 Three Questions 46
2.6 Positive Maps on Operator Systems 49
2.7 Supplementary Results and Exercises 52
2.8 Notes and References 62
Chapter 3. Completely Positive Maps 65
3.1 Some Basic Theorems 66
3.2 Exercises 72
3.3 Schwarz Inequalities 73
3.4 Positive Completions and Schur Products 76
3.5 The Numerical Radius 81
3.6 Supplementary Results and Exercises 85
3.7 Notes and References 94
Chapter 4. Matrix Means 101
4.1 The Harmonic Mean and the Geometric Mean • 103
4.2 Some Monotonicity and Convexity Theorems 111
4.3 Some Inequalities for Quantum Entropy 114
4.4 Furuta s Inequality 125
4.5 Supplementary Results and Exercises 129
4.6 Notes and References 136
vi CONTENTS
Chapter 5. Positive Definite Functions 141
5.1 Basic Properties 141
5.2 Examples 144
5.3 Loewner Matrices 153
5.4 Norm Inequalities for Means 160
5.5 Theorems of Herglotz and Bochner 165
5.6 Supplementary Results and Exercises 175
5.7 Notes and References 191
Chapter 6. Geometry of Positive Matrices 201
6.1 The Riemannian Metric 201
6.2 The Metric Space Pn 210
6.3 Center of Mass and Geometric Mean 215
6.4 Related Inequalities 222
6.5 Supplementary Results and Exercises 225
6.6 Notes and References 232
Bibliography 237
Index 247
Notation 253
|
| adam_txt |
Contents
Preface vii
Chapter 1. Positive Matrices 1
1.1 Characterizations 1
1.2 Some Basic Theorems 5
1.3 Block Matrices 12
1.4 Norm of the Schur Product 16
1.5 Monotonicity and Convexity 18
1.6 Supplementary Results and Exercises 23
1.7 Notes and References 29
Chapter 2. Positive Linear Maps 35
2.1 Representations 35
2.2 Positive Maps 36
2.3 Some Basic Properties of Positive Maps 38
2.4 Some Applications 43
2.5 Three Questions 46
2.6 Positive Maps on Operator Systems 49
2.7 Supplementary Results and Exercises 52
2.8 Notes and References 62
Chapter 3. Completely Positive Maps 65
3.1 Some Basic Theorems 66
3.2 Exercises 72
3.3 Schwarz Inequalities 73
3.4 Positive Completions and Schur Products 76
3.5 The Numerical Radius 81
3.6 Supplementary Results and Exercises 85
3.7 Notes and References 94
Chapter 4. Matrix Means 101
4.1 The Harmonic Mean and the Geometric Mean • 103
4.2 Some Monotonicity and Convexity Theorems 111
4.3 Some Inequalities for Quantum Entropy 114
4.4 Furuta's Inequality 125
4.5 Supplementary Results and Exercises 129
4.6 Notes and References 136
vi CONTENTS
Chapter 5. Positive Definite Functions 141
5.1 Basic Properties 141
5.2 Examples 144
5.3 Loewner Matrices 153
5.4 Norm Inequalities for Means 160
5.5 Theorems of Herglotz and Bochner 165
5.6 Supplementary Results and Exercises 175
5.7 Notes and References 191
Chapter 6. Geometry of Positive Matrices 201
6.1 The Riemannian Metric 201
6.2 The Metric Space Pn 210
6.3 Center of Mass and Geometric Mean 215
6.4 Related Inequalities 222
6.5 Supplementary Results and Exercises 225
6.6 Notes and References 232
Bibliography 237
Index 247
Notation 253 |
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| index_date | 2024-07-02T16:48:34Z |
| indexdate | 2024-07-09T20:53:58Z |
| institution | BVB |
| isbn | 9780691129181 0691129185 9780691168258 |
| language | English |
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| spelling | Bhatia, Rajendra 1952- Verfasser (DE-588)104344431 aut Positive definite matrices Rajendra Bhatia Princeton, NJ [u.a] Princeton Univ. Press 2007 IX, 254 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Princeton series in applied mathematics Includes bibliographical references and index Matrices Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015488667&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bhatia, Rajendra 1952- Positive definite matrices Matrices Matrix Mathematik (DE-588)4037968-1 gnd |
| subject_GND | (DE-588)4037968-1 |
| title | Positive definite matrices |
| title_auth | Positive definite matrices |
| title_exact_search | Positive definite matrices |
| title_exact_search_txtP | Positive definite matrices |
| title_full | Positive definite matrices Rajendra Bhatia |
| title_fullStr | Positive definite matrices Rajendra Bhatia |
| title_full_unstemmed | Positive definite matrices Rajendra Bhatia |
| title_short | Positive definite matrices |
| title_sort | positive definite matrices |
| topic | Matrices Matrix Mathematik (DE-588)4037968-1 gnd |
| topic_facet | Matrices Matrix Mathematik |
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