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Matrices of sign-solvable linear systems

Brualdi, Richard A.

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Matrices of sign-solvable linear systems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Matrices of sign-solvable linear systems/ Richard A. Brualdi, Bryan L. Shader.
作者:	Brualdi, Richard A.
其他作者:	Shader, Bryan L.
出版者:	Cambridge :Cambridge University Press, : 1995.,
面頁冊數:	xii, 298 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	Sign-solvability -- L-matrices -- Sign-solvability and digraphs -- S-matrices -- Beyond S*-matrices -- SNS-matrices -- S2NS-matrices -- External properties of L-Matrices -- The inverse sign pattern graph -- Sign stability -- Related topics.
標題:	Matrices. -
電子資源:	https://doi.org/10.1017/CBO9780511574733
ISBN:	9780511574733

Matrices of sign-solvable linear systems
Brualdi, Richard A.

Matrices of sign-solvable linear systems[electronic resource] /Richard A. Brualdi, Bryan L. Shader. - Cambridge :Cambridge University Press,1995. - xii, 298 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;116. - Cambridge tracts in mathematics ;116..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Sign-solvability -- L-matrices -- Sign-solvability and digraphs -- S-matrices -- Beyond S*-matrices -- SNS-matrices -- S2NS-matrices -- External properties of L-Matrices -- The inverse sign pattern graph -- Sign stability -- Related topics.

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.

ISBN: 9780511574733Subjects--Topical Terms:

516894
Matrices.

LC Class. No.: QA188 / .B79 1995

Dewey Class. No.: 512.9434

Matrices of sign-solvable linear systems
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520 $a 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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