Totally Nonnegative Matrices

Released on by Shaun M. Fallat
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  • Totally Nonnegative Matrices Book Detail

  • Author : Shaun M. Fallat
  • Release Date : 2011-04-11
  • Publisher : Princeton University Press
  • Genre : Mathematics
  • Pages : 265
  • ISBN 13 : 1400839017
  • File Size : 46,46 MB
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Totally Nonnegative Matrices by Shaun M. Fallat PDF Summary

Book Description: 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.

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Totally Nonnegative Matrices

Totally Nonnegative Matrices

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Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential

Totally Nonnegative Matrices

Totally Nonnegative Matrices

File Size : 47,47 MB
Total View : 946 Views
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Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential

Completely Positive Matrices

Completely Positive Matrices

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A real matrix is positive semidefinite if it can be decomposed as A = BBOC . In some applications the matrix B has to be elementwise nonnegative. If such a matr

Completely Positive Matrices

Completely Positive Matrices

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A real matrix is positive semidefinite if it can be decomposed as A=BB′. In some applications the matrix B has to be elementwise nonnegative. If such a matrix