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 Heavenly Mathematics by Shaun M. Fallat, Charles R. Johnson
Cover of the book Homology, Genes, and Evolutionary Innovation by Shaun M. Fallat, Charles R. Johnson
Cover of the book Thieves, Deceivers, and Killers by Shaun M. Fallat, Charles R. Johnson
Cover of the book The Genome Factor by Shaun M. Fallat, Charles R. Johnson
Cover of the book Aristotle's Politics by Shaun M. Fallat, Charles R. Johnson
Cover of the book Poverty Traps by Shaun M. Fallat, Charles R. Johnson
Cover of the book An Essay on Man by Shaun M. Fallat, Charles R. Johnson
Cover of the book Not Even Past by Shaun M. Fallat, Charles R. Johnson
Cover of the book Kierkegaard's Writings, XII, Volume II by Shaun M. Fallat, Charles R. Johnson
Cover of the book Alabama in Africa by Shaun M. Fallat, Charles R. Johnson
Cover of the book Economic and Financial Decisions under Risk by Shaun M. Fallat, Charles R. Johnson
Cover of the book The Dancing Lares and the Serpent in the Garden by Shaun M. Fallat, Charles R. Johnson
Cover of the book Making a Good Life by Shaun M. Fallat, Charles R. Johnson
Cover of the book Mathematical Modeling of Earth's Dynamical Systems by Shaun M. Fallat, Charles R. Johnson
Cover of the book Amazing Arachnids 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