Cambridge University Press, 1997. — 350 p. — ISBN: 0521571677
OCR.
This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.
Multidisciplinary applications from game theory, optimisation, mathematical programming, economics and statistics
Many results, most of them completely proved
Minimal prerequisites: each section of the book is self-contained and can be read independently
Contents:
Preface
Perron-Frobenius theory and matrix games
Doubly stochastic matrices
Inequalities
Conditionally positive definite matrices
Topics in combinatorial theory
Scaling problems and their applications
Special matrices in economic models
References
Index
Author index.