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Totally Nonnegative Matrices
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Totally Nonnegative Matrices

Shaun M. Fallat and Charles R. Johnson

Abstract

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 factorizatio ... More

Keywords: totally nonnegative matrices, nonnegativity, subdeterminants, bidiagonal factorization, totally positive matrices, variation diminution, spectral properties, determinantal inequalities, Hadamard products

Bibliographic Information

Print publication date: 2011 Print ISBN-13: 9780691121574
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691121574.001.0001

Authors

Affiliations are at time of print publication.

Shaun M. Fallat, author
University of Regina

Charles R. Johnson, author
College of William and Mary