| Description |
1 online resource (xviii, 205 pages) |
| Series |
Encyclopedia of mathematics and its applications ; v. 6. Section, Linear algebra |
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Encyclopedia of mathematics and its applications ; v. 6.
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Encyclopedia of mathematics and its applications. Section, Linear algebra.
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| Contents |
2.2 The Permanent Function as an Inner ProductProblems; CHAPTER 3 (0, 1)-Matrices; 3.1 Incidence Matrices; 3.2 Theorems of Frobenius and Konig; 3.3 Structure of Square (0, 1)-Matrices; 3.4 (0, 1)-Circulants; Problems; CHAPTER 4 Lower Bounds for Permanents; 4.1 Marshall Hall's Theorem; 4.2 (0, I)-Matrices; 4.3 Fully Indecomposable (0, I)-Matrices; 4.4 Nonnegative Matrices; 4.5 Positive Semi-definite Hermitian Matrices; Problems; CHAPTER 5 The van der Waerden Conjecture; 5.1 The Marcus-Newman Theory; 5.2 Properties of Minimizing Matrices; 5.3 Some Partial Results. Friedland's Theorem |
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5.4 A Conjecture of Marcus and Mine5.5 Lower Bounds for the Permanents of Doubly Stochastic Matrices; Problems; CHAPTER 6 Upper Bounds for Permanents; 6.1 From Muir to Jurkat and Ryser; 6.2 (0, I)-Matrices; 6.3 Nonnegative Matrices; 6.4 Complex Matrices; Problems; CHAPTER 7 Evaluation of Permanents; 7.1 Binet-Mine Method; 7.2 Ryser's Method; 7.3 Comparison of Evaluation Methods; Problems; CHAPTER 8 More about Permanents; 8.1 Other Results; 8.2 Some Applications of Permanents; 8.3 Conjectures and Unsolved Problems-Vintage 1965; 8.4 Conjectures and Unsolved Problems-A Current List; Problems |
| Summary |
The purpose of this book, which was first published in 1978, is to give a complete account of the theory of permanents, their history and applications. This volume was the first complete account of the theory of permanents, covering virtually the whole of the subject, a feature that no simple survey of the theory of matrices can even attempt. The work also contains many results stated without formal proofs. This book can be used as a textbook at the advanced undergraduate or graduate level. The only prerequisites are a standard undergraduate course in the theory of matrices and a measure of mathematical maturity |
| Notes |
Imprint and ISBN from label on title page verso. Imprint on t.p.: Reading, Mass. : Addison-Wesley, Advanced Book Program, 1978 |
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Publication taken over by Cambridge University Press in 1984 with a new copyright date |
| Bibliography |
Includes bibliographical references (pages 161-196) |
| Notes |
Includes indexes |
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Print version record |
| Subject |
Permanents (Matrices)
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Inequalities (Mathematics)
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MATHEMATICS -- Algebra -- Elementary.
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Inequalities (Mathematics)
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Permanents (Matrices)
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Matrix Mathematik
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Permanente
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Ungleichung
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Lineare Algebra
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| Form |
Electronic book
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| ISBN |
9781107266742 |
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1107266742 |
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9781107340688 |
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1107340683 |
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