Nonnegative Matrices and Applications

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.