Totally nonnegative matrices

Resource Information

The work Totally nonnegative matrices represents a distinct intellectual or artistic creation found in University of Missouri-St. Louis Libraries. This resource is a combination of several types including: Work, Language Material, Books.

Label

Totally nonnegative matrices

Statement of responsibility

Shaun M. Fallat, Charles R. Johnson

Creator

• Fallat, Shaun M

Contributor

• Johnson, Charles R

Subject

• MATHEMATICS -- Algebra | Linear
• MATHEMATICS -- Applied
• MATHEMATICS -- Matrices
• Non-negative matrices
• Non-negative matrices
• Electronic books

Language

eng

Summary

• "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"--
• ""Totally Nonnegative Matrices" is a comprehensive, modern treatment of the titled class of matrices that arise in very many ways. Methodological background is given, and elementary bidiagonal factorization is a featured tool. In addition to historical highlights and sources of interest, some of the major topics include: recognition, variation diminution, spectral structure, determinantal inequalities, Hadamard products, and completion problems"--

Member of

• Princeton series in applied mathematics

Assigning source

• Provided by publisher
• Provided by publisher

Cataloging source

N$T

Dewey number

512.9/434

Illustrations

illustrations

Index

index present

Language note

In English

LC call number

QA188

LC item number

.F35 2011eb

Literary form

non fiction

Nature of contents

• dictionaries
• bibliography

Series statement

Princeton series in applied mathematics