Totally Nonnegative Matrices

Totally Nonnegative Matrices

by Shaun M. Fallat, Charles R. Johnson
     
 

View All Available Formats & Editions

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.

Overview

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.

Editorial Reviews

Mathematical Reviews
This book is a very useful new reference on the subject of TN matrices and it will be of interest to researchers on matrix theory as well as to researchers of any field where total positivity has applications.
— Juan Manuel Pefia
Mathematical Reviews - Juan Manuel Pefia
This book is a very useful new reference on the subject of TN matrices and it will be of interest to researchers on matrix theory as well as to researchers of any field where total positivity has applications.
From the Publisher
"This book is a very useful new reference on the subject of TN matrices and it will be of interest to researchers on matrix theory as well as to researchers of any field where total positivity has applications."—Juan Manuel Pefia, Mathematical Reviews

Product Details

ISBN-13:
9781400839018
Publisher:
Princeton University Press
Publication date:
04/11/2011
Series:
Princeton Series in Applied Mathematics
Sold by:
Barnes & Noble
Format:
NOOK Book
Pages:
264
File size:
8 MB

Related Subjects

Meet the Author

Shaun M. Fallat is professor of mathematics and statistics at the University of Regina. Charles R. Johnson is the Class of 1961 Professor of Mathematics at the College of William & Mary.

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >