Matrices of Sign-Solvable Linear Systems

by Richard A. Brualdi, Bryan L. Shader

Overview

In a sign-solvable linear system, the signs of the coefficients determine the signs of some entries in the solution. This type of system is part of a larger study that helps researchers understand if properties of a matrix can be determined from combinatorial arrangements of its elements. In this book, the authors present the diffuse body of literature on sign-solvability as a coherent whole for the first time, giving many new results and proofs and establishing many new connections. Brualdi and Shader describe and comment on algorithms implicit in many of the proofs and their complexity. The book is self-contained, assuming familiarity only with elementary linear algebra and graph theory. Intended primarily for researchers in combinatorics and linear algebra, it should also be of interest to computer scientists, economists, physicists, chemists, and engineers.

Product Details

ISBN-13:	9780521105828
Publisher:	Cambridge University Press
Publication date:	04/02/2009
Series:	Cambridge Tracts in Mathematics , #116
Pages:	316
Product dimensions:	5.98(w) x 9.02(h) x 0.71(d)

Table of Contents

Preface; 1. Sign-solvability; Bibliography; 2. L-matrices; Bibliography; 3. Sign-solvability and digraphs; Bibliography; 4. S*-matrices; Bibliography; 5. Beyond S*-matrices; Bibliography; 6. SNS-matrices; Bibliography; 7. S2NS-matrices; Bibliography; 8. Extremal properties of L-matrices; Bibliography; 9. The inverse sign pattern graph; Bibliography; 10. Sign stability; Bibliography; 11. Related Topics; Bibliography; Master Bibliography; Index.

What People are Saying About This

From the Publisher

"The book is well written and quite readable. It should become an indispensable reference for anyone intersted in questions related to sign solvability of linear systems." Peter M. Gibson, SIAM Review

"...primarily for researchers in combinatorics and linear algebra, it should also be of interest to theoretical computer scientists, economists, physicists, chemists and engineers." Gerard Sierksma, Mathematical Review

Editorial Reviews

A unified and self-contained presentation of sign-solvability, revealing it as a beautiful interplay among combinatorics (especially graph theory), linear algebra, and theoretical computer science (combinatorial algorithms). The organization of the material affords new connections among various results in the literature, as well as giving new results and new and simpler proofs of previously established results. A noteworthy feature is the explicit description of algorithms that are implicit in many of the proofs, with commentary on their complexity. There are chapter bibliographies as well as a master bibliography. Primarily for researchers in combinatorics and linear algebra, but also of interest to theoretical computer scientists, economists, physicists, chemists, and engineers. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"The book is well written and quite readable. It should become an indispensable reference for anyone intersted in questions related to sign solvability of linear systems." Peter M. Gibson, SIAM Review

"...primarily for researchers in combinatorics and linear algebra, it should also be of interest to theoretical computer scientists, economists, physicists, chemists and engineers." Gerard Sierksma, Mathematical Review

From the Publisher