Totally Nonnegative Matrices
eBook - ePub

Totally Nonnegative Matrices

  1. 264 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Totally Nonnegative Matrices

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About This Book

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.

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Yes, you can access Totally Nonnegative Matrices by Shaun M. Fallat,Charles R. Johnson in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Princeton University Press
Year
2011
ISBN
9781400839018
Topic
Mathematics
Subtopic
Applied Mathematics
Index
Mathematics

Table of contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Dedication
  5. Contents
  6. List of Figures
  7. Preface
  8. Chapter 0. Introduction
  9. Chapter 1. Preliminary Results and Discussion
  10. Chapter 2. Bidiagonal Factorization
  11. Chapter 3. Recognition
  12. Chapter 4. Sign Variation of Vectors and TN Linear Transformations
  13. Chapter 5. The Spectral Structure of TN Matrices
  14. Chapter 6. Determinantal Inequalities for TN Matrices
  15. Chapter 7. Row and Column Inclusion and the Distribution of Rank
  16. Chapter 8. Hadamard Products and Powers of TN Matrices
  17. Chapter 9. Extensions and Completions
  18. Chapter 10. Other Related Topics on TN Matrices
  19. Bibliography
  20. List of Symbols
  21. Index