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Matrices of Sign-Solvable Linear Systems

$41.95

Part of Cambridge Tracts in Mathematics

  • Date Published: April 2009
  • availability: Available
  • format: Paperback
  • isbn: 9780521105828

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  • 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.

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    Product details

    • Date Published: April 2009
    • format: Paperback
    • isbn: 9780521105828
    • length: 316 pages
    • dimensions: 229 x 152 x 18 mm
    • weight: 0.47kg
    • contains: 7 b/w illus.
    • availability: 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.

  • Authors

    Richard A. Brualdi, University of Wisconsin, Madison

    Bryan L. Shader, University of Wyoming

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