Nonnegative Matrices and Applications

Nonnegative Matrices and Applications

by R. B. Bapat, T. E. S. Raghavan
     
 

This book presents an integrated treatment of the theory of nonnegative matrices, emphasizing connections with the themes of game theory, combinatorics, inequalities, optimization, and mathematical economics. Some related classes of positive matrices such as positive semidefinite matrices, M-matrices, P-matrices, and distance matrices are also discussed, but the main… See more details below

Overview

This book presents an integrated treatment of the theory of nonnegative matrices, emphasizing connections with the themes of game theory, combinatorics, inequalities, optimization, and mathematical economics. Some related classes of positive matrices such as positive semidefinite matrices, M-matrices, P-matrices, and distance matrices are also discussed, but the main emphasis is on entrywise nonnegative matrices. The book begins with the basics of the subject, such as the Perron-Frobenius Theorem. Only a minimal background in linear algebra is assumed, although familiarity with linear programming and statistics will be helpful in following some sections. Each of the later chapters is devoted to an area of applications, including doubly stochastic matrices (price fixing, scheduling, and the fair division problem), combinatorial matroids, and economics. These applications have been carefully chosen both for their elegant mathematical content and for their accessibility. The treatment is rigorous and almost all results are proved completely. About half of the material in the book presents standard topics in a novel fashion, the remaining portion reports many new results in matrix theory for the first time in a book form.

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Product Details

ISBN-13:
9780521118668
Publisher:
Cambridge University Press
Publication date:
08/20/2009
Series:
Encyclopedia of Mathematics and its Applications Series, #64
Edition description:
New Edition
Pages:
356
Product dimensions:
6.20(w) x 9.30(h) x 0.80(d)

Related Subjects

Table of Contents

Preface
1Perron-Frobenius theory and matrix games1
2Doubly stochastic matrices59
3Inequalities115
4Conditionally positive definite matrices161
5Topics in combinatorial theory196
6Scaling problems and their applications239
7Special matrices in economic models275
References315
Index329
Author Index333

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