Totally Nonnegative Matrices / / Charles R. Johnson, Shaun M. Fallat.

• Superior document: Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package
• VerfasserIn: Fallat, Shaun M.,; Johnson, Charles R.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2011]; ©2011
• Year of Publication: 2011
• Edition: Course Book
• Language: English
• Series: Princeton Series in Applied Mathematics ; 35
• Physical Description: 1 online resource (264 p.) :; 21 line illus. 3 tables.
• Other title: Frontmatter --; Contents --; List of Figures --; Preface --; Chapter 0. Introduction --; Chapter One. Preliminary Results and Discussion --; Chapter Two. Bidiagonal Factorization --; Chapter Three. Recognition --; Chapter Four. Sign Variation of Vectors and TN Linear Transformations --; Chapter Five. The Spectral Structure of TN Matrices --; Chapter Six. Determinantal Inequalities for TN Matrices --; Chapter Seven. Row and Column Inclusion and the Distribution of Rank --; Chapter Eight. Hadamard Products and Powers of TN Matrices --; Chapter Nine. Extensions and Completions --; Chapter Ten. Other Related Topics on TN Matrices --; Bibliography --; List of Symbols --; Index
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400839018; 9783110515831; 9783110442502
• DOI: 10.1515/9781400839018?locatt=mode:legacy
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Charles R. Johnson, Shaun M. Fallat.

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.