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: 7399

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: 8691

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.

Combinatorial Matrix Classes

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Author: Richard A. Brualdi

Publisher: Cambridge University Press

ISBN: 0521865654

Category: Mathematics

Page: 544

View: 4941

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.

The Chinese Roots of Linear Algebra

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Author: Roger Hart

Publisher: JHU Press

ISBN: 9780801899584

Category: Mathematics

Page: 304

View: 739

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: 135164405X

Category: Mathematics

Page: 1612

View: 7768

Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.

Interfaces

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Industrial management

Page: N.A

View: 9090

Permanents

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Author: Henryk Minc

Publisher: Cambridge University Press

ISBN: 9780521302265

Category: Mathematics

Page: 224

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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.

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: 2015

Match

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Chemistry

Page: N.A

View: 6601

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: 4444

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: 6078

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.

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: 3604

Topics in Algebraic Graph Theory

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Author: Lowell W. Beineke,Robin J. Wilson

Publisher: Cambridge University Press

ISBN: 9780521801973

Category: Mathematics

Page: 276

View: 6363

There is no other book with such a wide scope of both areas of algebraic graph theory.

Noncommutative Rational Series with Applications

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Author: Jean Berstel,Christophe Reutenauer

Publisher: Cambridge University Press

ISBN: 0521190223

Category: Mathematics

Page: 248

View: 3878

A modern account of the subject and its applications. Excellent resource for those working in algebra and theoretical computer science.

Non-negative Matrices and Markov Chains

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Author: E. Seneta

Publisher: Springer Science & Business Media

ISBN: 9780387297651

Category: Mathematics

Page: 279

View: 1246

A Springer classic originally published in 1981, available for the first time in paperback. 7 pages of new material have been added, plus an updated bibliography and errata list.

Maximum and Minimum Principles

A Unified Approach with Applications

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Author: M. J. Sewell

Publisher: CUP Archive

ISBN: 9780521332446

Category: Mathematics

Page: 468

View: 7115

This book provides a unified account of the theory required to establish upper and lower bounds.

Volterra Integral and Functional Equations

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Author: G. Gripenberg,S. O. Londen,O. Staffans

Publisher: Cambridge University Press

ISBN: 9780521372893

Category: Mathematics

Page: 701

View: 5273

This book looks at the theories of Volterra integral and functional equations.