Matrices of Sign-Solvable Linear Systems

Richard A. Brualdi, Bryan L. Shader (Autoren)

Buch | Hardcover

316 Seiten

1995
Cambridge University Press (Verlag)
978-0-521-48296-7 (ISBN)

Artikel merken

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.

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.

Erscheint lt. Verlag	29.9.1995
Reihe/Serie	Cambridge Tracts in Mathematics
Zusatzinfo	7 Line drawings, unspecified
Verlagsort	Cambridge
Sprache	englisch
Maße	159 x 234 mm
Gewicht	552 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
ISBN-10	0-521-48296-8 / 0521482968
ISBN-13	978-0-521-48296-7 / 9780521482967
Zustand	Neuware