Totally nonnegative matrices
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Author
Contributions
- Johnson, Charles R. - Contributor
Publication
2011 - Princeton University Press, Princeton, New Jersey
Language
English
Word Count
62,000 words, Guess
Page Count
248 pages
Identifiers
- Open LibraryOL25075397M
- ISBN-139780691121574
- OCLC Control Number679940604
- OCLC Control Numbertotallynonnegati00fall
- Library of Congress Control Number2010052042
Classifications
- DDC512.9/434
- LCCQA188 .F35 2011
Description
"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"-- "Totally Nonnegative Matrices" is a comprehensive, modern treatment of the titled class of matrices that arise in very many ways. Methodological background is given, and elementary bidiagonal factorization is a featured tool. In addition to historical highlights and sources of interest, some of the major topics include: recognition, variation diminution, spectral structure, determinantal inequalities, Hadamard products, and completion problems. "--
Subjects
Topics
Series Statement
- Princeton series in applied mathematics
Other Editions
- Totally nonnegative matrices
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