Matrices of Sign-Solvable Linear Systems
Matrices of Sign-Solvable Linear Systems
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.
Reviews & endorsements
"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
Product details
April 2009Paperback
9780521105828
316 pages
229 × 152 × 18 mm
0.47kg
7 b/w illus.
Available
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.
