Totally Nonnegative Matrices

Shaun M. Fallat, Charles R. Johnson

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English

Princeton University Press
11 July 2011

Applied mathematics

Series: Princeton Series in Applied Mathematics

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.

By: Shaun M. Fallat, Charles R. Johnson
Imprint: Princeton University Press
Country of Publication: United States
Volume: 35
Dimensions: Height: 235mm, Width: 152mm, Spine: 23mm
Weight: 482g
ISBN: 9780691121574
ISBN 10: 0691121575
Series: Princeton Series in Applied Mathematics
Pages: 264
Publication Date: 11 July 2011
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Reviews for Totally Nonnegative Matrices

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