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 Would You Kill the Fat Man? by Shaun M. Fallat, Charles R. Johnson
Cover of the book A Short History of Celebrity by Shaun M. Fallat, Charles R. Johnson
Cover of the book Causation in Science by Shaun M. Fallat, Charles R. Johnson
Cover of the book Computational Economics by Shaun M. Fallat, Charles R. Johnson
Cover of the book Unequal Gains by Shaun M. Fallat, Charles R. Johnson
Cover of the book Dividing Lines by Shaun M. Fallat, Charles R. Johnson
Cover of the book How Round Is Your Circle? by Shaun M. Fallat, Charles R. Johnson
Cover of the book Getting Incentives Right by Shaun M. Fallat, Charles R. Johnson
Cover of the book Debtor Nation by Shaun M. Fallat, Charles R. Johnson
Cover of the book Three Worlds of Relief by Shaun M. Fallat, Charles R. Johnson
Cover of the book Caliphate Redefined by Shaun M. Fallat, Charles R. Johnson
Cover of the book Ethics in the Real World by Shaun M. Fallat, Charles R. Johnson
Cover of the book Degenerate Diffusion Operators Arising in Population Biology (AM-185) by Shaun M. Fallat, Charles R. Johnson
Cover of the book The Founders on Religion by Shaun M. Fallat, Charles R. Johnson
Cover of the book The Enlightenment 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