Nonnegative matrices and applications

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 new results in matrix theory are presented for the first time in book form, while more standard topics are presented in a novel fashion.

The treatment is rigorous and almost all results are proved completely.

These new 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.