This book provides an integrated treatment of the theory of nonnegative matrices and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimization and mathematical economics. The authors have chosen the wide variety of applications, which include price fixing, scheduling, and the fair division problem, both for their elegant mathematical content and for their accessibility to students with minimal preparation. They present many new results in matrix theory for the first time in book form, while they present more standard topics 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.
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Book Description
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"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
Book Description
Nonnegative matrices (matrices with only positive numbers or zero as entries) arise in a variety of applications. This book provides an integrated approach to this area, emphasizing connections with game theory, combinatorics, optimization, mathematical programming, mathematical economics and statistics. The treatment is rigorous and almost all results are proved completely. Researchers in these areas will find many new results and applications in this book. The minimal prerequisites will also make it accessible to graduate students.
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
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First Sentence:
The Perron-Frobenius Theorem is central to the theory of nonnegative matrices. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Alexandroff Inequality, Birkhoff-von Neumann Theorem, Duality Theorem, Information Inequality, Brouwer's Fixed Point Theorem, Frobenius Normal Form, Kronecker Index Theorem, Perron's Theorem, Proof Suppose, Air Force, Matrix-Tree Theorem, Proof By Theorem, Series-Parallel Inequality, Fiedler's Inequality, Jacobian Conjecture, Oppenheim's Inequality, Proof By Lemma, Proof First, Use Exercise New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
The Perron-Frobenius Theorem is central to the theory of nonnegative matrices. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Alexandroff Inequality, Birkhoff-von Neumann Theorem, Duality Theorem, Information Inequality, Brouwer's Fixed Point Theorem, Frobenius Normal Form, Kronecker Index Theorem, Perron's Theorem, Proof Suppose, Air Force, Matrix-Tree Theorem, Proof By Theorem, Series-Parallel Inequality, Fiedler's Inequality, Jacobian Conjecture, Oppenheim's Inequality, Proof By Lemma, Proof First, Use Exercise New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 53
books:
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18
books
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- Linear Algebra: Supplementary Notes & Problems by E. L. Cohen in Back Matter (1), and Back Matter (2)
- Incline Algebra and Applications (Ellis Horwood Series in Engineering Science) by Z. -Q Cao in Back Matter
- Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications) by Richard A. Brualdi in Back Matter
- Discrete Multivariate Analysis: Theory and Practice by Yvonne M. Bishop in Back Matter
- Heckscher-Ohlin Trade Theory by Eli F. Heckscher in Back Matter
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- Combinatorial Matrix Classes (Encyclopedia of Mathematics and its Applications) by Richard A. Brualdi on page 500, and Back Matter
- Positive Definite Matrices (Princeton in Applied Mathematics) by Rajendra Bhatia on page 196, and Back Matter
- Analysis of Variance for Random Models, Volume 2: Unbalanced Data: Theory, Methods, Applications, and Data Analysis by Hardeo Sahai on page 10, and Back Matter
- Geometric Tomography (Encyclopedia of Mathematics and its Applications) by Richard J. Gardner in Front Matter
- Positive Transfer Operators and Decay of Correlations (Advanced Series in Nonlinear Dynamics, Volume 16) by Viviane Baladi in Back Matter
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