Matrices of Sign-Solvable Linear Systems (Cambridge Tracts in Mathematics, Series Number 116) 1st Edition by Richard A. Brualdi (PDF)

Description

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.

User’s Reviews

Editorial Reviews: 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”…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 Book Description The large and diffuse body of literature connected with sign-solvability is presented as a coherent whole for the first time in this book.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I’m not really a mathematician at heart. I use math and enjoy using it, but never really learned to love it for its own sake. In other words, this book wasn’t written for me.I work with combinatoric problems a fair bit, and hoped that sign-solvable systems (SSS) would be directly applicable to some of my work. I also look at questions where sloppy data prevent exact solutions – if a technique promises at least partial answers when precise answers aren’t available, it has my interest. The SSS premise is that, in some cases, I can tell whether parts of my answer are positive, negative, or zero, knowing only whether the inputs were positive, negative, or zero. The simplified character of the questions and answers could possibly work well in special computing environments that I use. I really wanted to like this book and its content.I just wasn’t able to connect these abstractions to my real world, though. The focus of this book is on the abstract structures behind SSS, and on formal proofs about specific features of special cases.This book does have a practical side. It specifies a number of algorithms for handling sign-solvable systems of various sorts. It would take a lot of effort to reduce these algorithms to practice, but the information is all there. As books of pure advanced math go, this one seems relatively clear and approachable.Perhaps a more astute reader than me can connect SSS to problems of practical interest. Perhaps, some day, I’ll take the time to work through this book in detail. These days, though, I can’t spend a lot of time away from the problems I need to solve. Building up a working knowledge of SSS from this book would take intense effort. I really have to put my effort elsewhere.

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