Totally Nonnegative Matrices

Nonfiction, Science & Nature, Mathematics, Matrices, Applied
Cover of the book Totally Nonnegative Matrices by Shaun M. Fallat, Charles R. Johnson, Princeton University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Shaun M. Fallat, Charles R. Johnson ISBN: 9781400839018
Publisher: Princeton University Press Publication: April 11, 2011
Imprint: Princeton University Press Language: English
Author: Shaun M. Fallat, Charles R. Johnson
ISBN: 9781400839018
Publisher: Princeton University Press
Publication: April 11, 2011
Imprint: Princeton University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Princeton University Press

Cover of the book Confucianism as a World Religion by Shaun M. Fallat, Charles R. Johnson
Cover of the book Discoverers of the Universe by Shaun M. Fallat, Charles R. Johnson
Cover of the book Managing Egypt's Poor and the Politics of Benevolence, 1800-1952 by Shaun M. Fallat, Charles R. Johnson
Cover of the book Paths of Fire by Shaun M. Fallat, Charles R. Johnson
Cover of the book A History of Judaism by Shaun M. Fallat, Charles R. Johnson
Cover of the book School Choice by Shaun M. Fallat, Charles R. Johnson
Cover of the book On the Origins of Jewish Self-Hatred by Shaun M. Fallat, Charles R. Johnson
Cover of the book The Free-Market Innovation Machine by Shaun M. Fallat, Charles R. Johnson
Cover of the book The Son Also Rises by Shaun M. Fallat, Charles R. Johnson
Cover of the book On Global Justice by Shaun M. Fallat, Charles R. Johnson
Cover of the book Byzantium by Shaun M. Fallat, Charles R. Johnson
Cover of the book Discrete and Computational Geometry by Shaun M. Fallat, Charles R. Johnson
Cover of the book The Correspondence of Henry D. Thoreau by Shaun M. Fallat, Charles R. Johnson
Cover of the book Statistical Mechanics in a Nutshell by Shaun M. Fallat, Charles R. Johnson
Cover of the book Searching for the Oldest Stars by Shaun M. Fallat, Charles R. Johnson
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy