Matrices of sign-solvable linear systems
著者
書誌事項
Matrices of sign-solvable linear systems
（Cambridge tracts in mathematics, 116）
Cambridge University Press, 2009, c1995
- : pbk.
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注記
Includes bibliographical reference (p. 289-293) and index
"First published 1995, This digitally printed version 2009" -- T.p. verso
"Paperback Re-issue" -- Back cover
内容説明・目次
内容説明
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.
目次
- 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.
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