Matrices of Sign-Solvable Linear Systems [Paperback]

The large and diffuse body of literature connected with sign-solvability is presented as a coherent whole for the first time in this book.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.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.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. Brul#