Matrices of Sign-Solvable Linear Systems

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

Richard A. Brualdi (Author), Bryan L. Shader (Author)

9780521105828, Cambridge University Press

Paperback / softback, published 2 April 2009

316 pages, 7 b/w illus.
22.9 x 15.2 x 1.8 cm, 0.47 kg

"...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

The sign-solvability of a linear system implies that the signs of the entries of the solution are determined solely on the basis of the signs of the coefficients of the system. That it might be worthwhile and possible to investigate such linear systems was recognised by Samuelson in his classic book Foundations of Economic Analysis. Sign-solvability is part of a larger study which seeks to understand the special circumstances under which an algebraic, analytic or geometric property of a matrix can be determined from the combinatorial arrangement of the positive, negative and zero elements of the matrix. The large and diffuse body of literature connected with sign-solvability is presented as a coherent whole for the first time in this book, displaying it as a beautiful interplay between combinatorics and linear algebra. One of the features of this book is that algorithms that are implicit in many of the proofs have been explicitly described and their complexity has been commented on.

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.

Subject Areas: Algebra [PBF]