Nonnegative Matrices and Applications

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Author: R. B. Bapat,T. E. S. Raghavan

Publisher: Cambridge University Press

ISBN: 9780521571678

Category: Mathematics

Page: 336

View: 4934

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.

The Mutually Beneficial Relationship of Graphs and Matrices

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Author: Richard A. Brualdi

Publisher: American Mathematical Soc.

ISBN: 0821853155

Category: Mathematics

Page: 96

View: 7072

Graphs and matrices enjoy a fascinating and mutually beneficial relationship. This interplay has benefited both graph theory and linear algebra. In one direction, knowledge about one of the graphs that can be associated with a matrix can be used to illuminate matrix properties and to get better information about the matrix. Examples include the use of digraphs to obtain strong results on diagonal dominance and eigenvalue inclusion regions and the use of the Rado-Hall theorem to deduce properties of special classes of matrices. Going the other way, linear algebraic properties of one of the matrices associated with a graph can be used to obtain useful combinatorial information about the graph. The adjacency matrix and the Laplacian matrix are two well-known matrices associated to a graph, and their eigenvalues encode important information about the graph. Another important linear algebraic invariant associated with a graph is the Colin de Verdiere number, which, for instance, characterizes certain topological properties of the graph. This book is not a comprehensive study of graphs and matrices. The particular content of the lectures was chosen for its accessibility, beauty, and current relevance, and for the possibility of enticing the audience to want to learn more.

The Chinese Roots of Linear Algebra

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Author: Roger Hart

Publisher: JHU Press

ISBN: 9780801899584

Category: Mathematics

Page: 304

View: 7205

Mathematicians and historians of mathematics and science will find in The Chinese Roots of Linear Algebra new ways to conceptualize the intellectual development of linear algebra.

Handbook of Discrete and Combinatorial Mathematics

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Author: Kenneth H. Rosen

Publisher: CRC Press

ISBN: 9780849301490

Category: Mathematics

Page: 1408

View: 4904

The importance of discrete and combinatorial mathematics continues to increase as the range of applications to computer science, electrical engineering, and the biological sciences grows dramatically. Providing a ready reference for practitioners in the field, the Handbook of Discrete and Combinatorial Mathematics, Second Edition presents additional material on Google's matrix, random graphs, geometric graphs, computational topology, and other key topics. New chapters highlight essential background information on bioinformatics and computational geometry. Each chapter includes a glossary, definitions, facts, examples, algorithms, major applications, and references.

Combinatorial Matrix Classes

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Author: Richard A. Brualdi

Publisher: Cambridge University Press

ISBN: 0521865654

Category: Mathematics

Page: 544

View: 1695

A natural sequel to the author's previous book Combinatorial Matrix Theory written with H. J. Ryser, this is the first book devoted exclusively to existence questions, constructive algorithms, enumeration questions, and other properties concerning classes of matrices of combinatorial significance. Several classes of matrices are thoroughly developed including the classes of matrices of 0's and 1's with a specified number of 1's in each row and column (equivalently, bipartite graphs with a specified degree sequence), symmetric matrices in such classes (equivalently, graphs with a specified degree sequence), tournament matrices with a specified number of 1's in each row (equivalently, tournaments with a specified score sequence), nonnegative matrices with specified row and column sums, and doubly stochastic matrices. Most of this material is presented for the first time in book format and the chapter on doubly stochastic matrices provides the most complete development of the topic to date.

Handbook of Linear Algebra

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Author: Leslie Hogben

Publisher: CRC Press

ISBN: 1420010573

Category: Mathematics

Page: 1400

View: 4671

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research. The book features an accessible layout of parts, chapters, and sections, with each section containing definition, fact, and example segments. The five main parts of the book encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, applications of linear algebra to various mathematical and nonmathematical disciplines, and software packages for linear algebra computations. Within each section, the facts (or theorems) are presented in a list format and include references for each fact to encourage further reading, while the examples illustrate both the definitions and the facts. Linearization often enables difficult problems to be estimated by more manageable linear ones, making the Handbook of Linear Algebra essential reading for professionals who deal with an assortment of mathematical problems.

Interfaces

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Industrial management

Page: N.A

View: 7302

Positive Systems

Proceedings of the ... Multidisciplinary International Symposium on Positive Systems, Theory and Applications (POSTA ...)

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematical models

Page: N.A

View: 2342

Match

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Chemistry

Page: N.A

View: 8292

Matrix Theory

Basic Results and Techniques

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Author: Fuzhen Zhang

Publisher: Springer Science & Business Media

ISBN: 1461410991

Category: Mathematics

Page: 399

View: 2520

The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains ten chapters covering various topics ranging from similarity and special types of matrices to Schur complements and matrix normality. This book can be used as a textbook or a supplement for a linear algebra and matrix theory class or a seminar for senior undergraduate or graduate students. The book can also serve as a reference for instructors and researchers in the fields of algebra, matrix analysis, operator theory, statistics, computer science, engineering, operations research, economics, and other fields. Major changes in this revised and expanded second edition: -Expansion of topics such as matrix functions, nonnegative matrices, and (unitarily invariant) matrix norms -A new chapter, Chapter 4, with updated material on numerical ranges and radii, matrix norms, and special operations such as the Kronecker and Hadamard products and compound matrices -A new chapter, Chapter 10, on matrix inequalities, which presents a variety of inequalities on the eigenvalues and singular values of matrices and unitarily invariant norms.

Combinatorial Matrix Theory

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Author: Richard A. Brualdi,Herbert J. Ryser

Publisher: Cambridge University Press

ISBN: 9780521322652

Category: Mathematics

Page: 367

View: 8928

The book deals with the many connections between matrices, graphs, diagraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorical properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix and Latin squares. The book ends by considering algebraic characterizations of combinatorical properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jorda Canonical Form.

Permanents

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Author: Henryk Minc

Publisher: Cambridge University Press

ISBN: 9780521302265

Category: Mathematics

Page: 224

View: 1879

The purpose of this book, which was first published in 1978, is to give a complete account of the theory of permanents, their history and applications. This volume was the first complete account of the theory of permanents, covering virtually the whole of the subject, a feature that no simple survey of the theory of matrices can even attempt. The work also contains many results stated without formal proofs. This book can be used as a textbook at the advanced undergraduate or graduate level. The only prerequisites are a standard undergraduate course in the theory of matrices and a measure of mathematical maturity.

Annales de L'I.H.P.

Probabilités et statistiques

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 2684

Nonnegative matrices in the mathematical sciences

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Author: Abraham Berman,Robert J. Plemmons

Publisher: Academic Pr

ISBN: N.A

Category: Mathematics

Page: 316

View: 6515

Matrices which leave a cone invariant; Monnegative matrices; Semigroups of nonnegative matrices; Symmetric nonnegative matrices; Generalized inverse-positivity; M-Matrices; Iterative methods for linear systems; Finite markov chains; Input-output analysis in economics; The linear complementarity problem.

Matrices and Graphs in Geometry

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Author: Miroslav Fiedler

Publisher: Cambridge University Press

ISBN: 0521461936

Category: Mathematics

Page: 197

View: 9385

This series is devoted to significant topics or themes that have wide application in mathematics or mathematical science and for which a detailed development of the abstract theory is less important than a thorough and concrete exploration of the implications and applications. Books in the Encyclopedia of Mathematics and Its Applications cover their subjects comprehensively. Less important results may be summarized as exercises at the ends of chapters. Each book contains an extensive bibliography. Thus the volumes are encyclopedic references or manageable guides to major subjects.

Encyclopedia of Optimization

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Author: Christodoulos A. Floudas,Panos M. Pardalos

Publisher: Springer Science & Business Media

ISBN: 0792369327

Category: Mathematics

Page: 3200

View: 6727

Optimization problems are widespread in the mathematical modeling of real world systems and their applications arise in all branches of science, applied science and engineering. The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics in order to show the spectrum of recent research activities and the richness of ideas in the development of theories, algorithms and the applications of optimization. It is directed to a diverse audience of students, scientists, engineers, decision makers and problem solvers in academia, business, industry, and government. Please note that this publication is available as print only OR online only OR print + online set. Save 75% of the online list price when purchasing the bundle.