Matrices & Determinants
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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.Synopsis
An integrated approach for new graduate students, emphasising connections with game theory, optimisation, mathematical programming and statistics.
Editorials
From the Publisher
"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 98hBook Details
Published
August 1, 2009
Publisher
Cambridge University Press
Pages
356
Format
Paperback
ISBN
9780521118668