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Matrices of Sign-Solvable Linear Systems: 116 (Cambridge Tracts in Mathematics, Series Number 116) - Hardcover
Synopsis
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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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, displaying it as a beautiful interplay between combinatorics and linear algebra.
"About this title" may belong to another edition of this title.
- PublisherCambridge University Press
- Publication date1995
- ISBN 10 0521482968
- ISBN 13 9780521482967
- BindingHardcover
- LanguageEnglish
- Number of pages316
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Matrices of Sign-Solvable Linear Systems. Cambridge Tracts in Mathematics, Volume 116
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Matrices of Sign-Solvable Linear Systems (Cambridge Tracts in Mathematics, Series Number 116)
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ISBN 13: 9780521482967
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Matrices of Sign-Solvable Linear Systems
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Matrices of Sign-Solvable Linear Systems (Cambridge Tracts in Mathematics) (Volume 116)
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ISBN 13: 9780521482967
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Matrices of Sign-Solvable Linear Systems (Cambridge Tracts in Mathematics)
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ISBN 10: 0521482968
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Matrices of Sign-Solvable Linear Systems
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Hard Cover. Condition: Very Good. Dust Jacket Condition: Good. First Edition. Advanced math text, presenting the diffuse literature connected to sign-solvability "as a coherent whole.a beautiful interplay between combinatorics (especially graph theory) and linear algebra." Publisher's Tracts in Mathematics series. Hardcover in jacket, as pictured. Light wear to book; jacket a bit rubbed with faded spine; name/address label (of one co-author's colleague) on free endsheet. Text clean; xii, 298 pages; bibliographies, index, many equations & figures. Size: Octavo. Seller Inventory # x1288
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Hardcover. Condition: new. Hardcover. 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. 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. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Seller Inventory # 9780521482967
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