Synopses & Reviews
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.
Review
"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
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
Synopsis
The large and diffuse body of literature connected with sign-solvability is presented as a coherent whole for the first time in this book.
Synopsis
In a sign-solvable linear system, some qualities of the solution are determined solely by the signs of the coefficients. Paul Samuelson extolled the use of such investigations in economics; applications have also been found in chemistry and physics. This book presents the diffuse field of sign-solvability as a coherent whole for the first time, giving many new results and establishing many new connections. Algorithms implicit in many of the proofs are explicitly described. Intended primarily for researchers in combinatorics and linear algebra, this self-contained account will also interest computer scientists, economists, physicists, chemists, and engineers.
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.