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  3. Matrices of Sign-Solvable Linear Systems
  • Cited by 76
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    • Publisher:
      Cambridge University Press
      Publication date:
      February 2010
      September 1995
      ISBN:
      9780511574733
      9780521482967
      9780521105828
      DOI:
      https://doi.org/10.1017/CBO9780511574733
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.552kg, 316 Pages
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.47kg, 316 Pages
      • Subjects:
      Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding
      Series:
      Cambridge Tracts in Mathematics (116)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding
    Series:
    Cambridge Tracts in Mathematics (116)
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    Book description

    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.

    Reviews

    "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

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