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.
Rezensionen / Stimmen
"It is a great work; great by its dimensions, written with extreme love and care, concentrating the knowledge of a generation which was supreme in the history of matrix theory. It is a very illuminating and highly readable exposition of interesting topics which are of great relevance both to theory and applications." Mathematical Reviews Clippings 98h
Reihe
Sprache
Verlagsort
Zielgruppe
Illustrationen
Maße
Höhe: 240 mm
Breite: 161 mm
Dicke: 24 mm
Gewicht
ISBN-13
978-0-521-57167-8 (9780521571678)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
Indian Statistical Institute, New Delhi
University of Illinois, Chicago
Preface; 1. Perron-Frobenius theory and matrix games; 2. Doubly stochastic matrices; 3. Inequalities; 4. Conditionally positive definite matrices; 5. Topics in combinatorial theory; 6. Scaling problems and their applications; 7. Special matrices in economic models; References; Index; Author index.
