Synopses & Reviews
Presents sign-solvability and its applications as a coherent whole; includes many new results.
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 numerous 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
1. Sign-solvability; 2. L-matrices; 3. Sign-solvability and digraphs; 4. S-matrices; 5. Beyond S*-matrices; 6. SNS-matrices; 7. S2NS-matrices; 8. External properties of L-Matrices; 9. The inverse sign pattern graph; 10. Sign stability; 11. Related topics.