Nonnegative Matrices In The Mathematical Sciences
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Nonnegative Matrices In The Mathematical Sciences
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Author : Abraham Berman
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Nonnegative Matrices In The Mathematical Sciences written by Abraham Berman and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Nonnegative Matrices in the Mathematical Sciences provides information pertinent to the fundamental aspects of the theory of nonnegative matrices. This book describes selected applications of the theory to numerical analysis, probability, economics, and operations research. Organized into 10 chapters, this book begins with an overview of the properties of nonnegative matrices. This text then examines the inverse-positive matrices. Other chapters consider the basic approaches to the study of nonnegative matrices, namely, geometrical and combinatorial. This book discusses as well some useful ideas from the algebraic theory of semigroups and considers a canonical form for nonnegative idempotent matrices and special types of idempotent matrices. The final chapter deals with the linear complementary problem (LCP). This book is a valuable resource for mathematical economists, mathematical programmers, statisticians, mathematicians, and computer scientists.
Nonnegative Matrices Positive Operators And Applications
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Author : Jiu Ding
language : en
Publisher: World Scientific Publishing Company
Release Date : 2009-08-24
Nonnegative Matrices Positive Operators And Applications written by Jiu Ding and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-24 with Mathematics categories.
Nonnegative matrices and positive operators are widely applied in science, engineering, and technology. This book provides the basic theory and several typical modern science and engineering applications of nonnegative matrices and positive operators, including the fundamental theory, methods, numerical analysis, and applications in the Google search engine, computational molecular dynamics, and wireless communications. Unique features of this book include the combination of the theories of nonnegative matrices and positive operators as well as the emphasis on applications of nonnegative matrices in the numerical analysis of positive operators, such as Markov operators and Frobenius–Perron operators both of which play key roles in the statistical and stochastic studies of dynamical systems. It can be used as a textbook for an upper level undergraduate or beginning graduate course in advanced matrix theory and/or positive operators as well as for an advanced topics course in operator theory or ergodic theory. In addition, it serves as a good reference for researchers in mathematical sciences, physical sciences, and engineering.
Nonnegative Matrices In Dynamic Systems
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Author : Abraham Berman
language : en
Publisher: Wiley-Interscience
Release Date : 1989
Nonnegative Matrices In Dynamic Systems written by Abraham Berman and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
This work applies the theory of nonnegative matrices to problems arising in positive differential and control systems. There is a concise review of requisite material in convex analysis and matrix theory, as well as a detailed review of linear differential and control systems. Exposition incorporates simple real-world dynamic models to better illustrate various aspects of the theory being developed. Contains exercises.
Nonnegative Matrices And Applicable Topics In Linear Algebra
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Author : Alexander Graham
language : en
Publisher: Dover Publications
Release Date : 2019-11-13
Nonnegative Matrices And Applicable Topics In Linear Algebra written by Alexander Graham and has been published by Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-13 with Mathematics categories.
Nonnegative matrices is an increasingly important subject in economics, control theory, numerical analysis, Markov chains, and other areas. This concise treatment is directed toward undergraduates who lack specialized knowledge at the postgraduate level of mathematics and related fields, such as mathematical economics and operations research. An Introductory Survey encompasses some aspects of matrix theory and its applications and other relevant topics in linear algebra, including certain facets of graph theory. Subsequent chapters cover various points of the theory of normal matrices, comprising unitary and Hermitian matrices, and the properties of positive definite matrices. An exploration of the main topic, nonnegative matrices, is followed by a discussion of M-matrices. The final chapter examines stochastic, genetic, and economic models. The important concepts are illustrated by simple worked examples. Problems appear at the conclusion of most chapters, with solutions at the end of the book.
Totally Nonnegative Matrices
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Author : Shaun M. Fallat
language : en
Publisher: Princeton University Press
Release Date : 2022-12-13
Totally Nonnegative Matrices written by Shaun M. Fallat and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-13 with Mathematics categories.
Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, historical highlights of key ideas, and specialized topics. The book uses classical and ad hoc tools, but a unifying theme is the elementary bidiagonal factorization, which has emerged as the single most important tool for this particular class of matrices. Recent work has shown that bidiagonal factorizations may be viewed in a succinct combinatorial way, leading to many deep insights. Despite slow development, bidiagonal factorizations, along with determinants, now provide the dominant methodology for understanding total nonnegativity. The remainder of the book treats important topics, such as recognition of totally nonnegative or totally positive matrices, variation diminution, spectral properties, determinantal inequalities, Hadamard products, and completion problems associated with totally nonnegative or totally positive matrices. The book also contains sample applications, an up-to-date bibliography, a glossary of all symbols used, an index, and related references.
Nonnegative Matrices And Applications
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Author : R. B. Bapat
language : en
Publisher: Cambridge University Press
Release Date : 1997-03-28
Nonnegative Matrices And Applications written by R. B. Bapat and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-03-28 with Mathematics categories.
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.
Non Negative Matrices And Markov Chains
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Author : E. Seneta
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-02
Non Negative Matrices And Markov Chains written by E. Seneta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-02 with Mathematics categories.
Since its inception by Perron and Frobenius, the theory of non-negative matrices has developed enormously and is now being used and extended in applied fields of study as diverse as probability theory, numerical analysis, demography, mathematical economics, and dynamic programming, while its development is still proceeding rapidly as a branch of pure mathematics in its own right. While there are books which cover this or that aspect of the theory, it is nevertheless not uncommon for workers in one or another branch of its development to be unaware of what is known in other branches, even though there is often formal overlap. One of the purposes of this book is to relate several aspects of the theory, insofar as this is possible. The author hopes that the book will be useful to mathematicians; but in particular to the workers in applied fields, so the mathematics has been kept as simple as could be managed. The mathematical requisites for reading it are: some knowledge of real-variable theory, and matrix theory; and a little knowledge of complex-variable; the emphasis is on real-variable methods. (There is only one part of the book, the second part of 55.5, which is of rather specialist interest, and requires deeper knowledge.) Appendices provide brief expositions of those areas of mathematics needed which may be less g- erally known to the average reader.
The Mutually Beneficial Relationship Of Graphs And Matrices
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Author : Richard A. Brualdi
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-07-06
The Mutually Beneficial Relationship Of Graphs And Matrices written by Richard A. Brualdi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-06 with Mathematics categories.
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.
Matrix Iterative Analysis
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Author : Richard S Varga
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-05
Matrix Iterative Analysis written by Richard S Varga and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-05 with Mathematics categories.
This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorporated in the revision, and in other places, new material has been added to the chapters in the form of additional up-to-date references and some recent theorems to give readers some new directions to pursue.
Matrix Algebra From A Statistician S Perspective
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Author : David A. Harville
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-27
Matrix Algebra From A Statistician S Perspective written by David A. Harville and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-27 with Mathematics categories.
A knowledge of matrix algebra is a prerequisite for the study of much of modern statistics, especially the areas of linear statistical models and multivariate statistics. This reference book provides the background in matrix algebra necessary to do research and understand the results in these areas. Essentially self-contained, the book is best-suited for a reader who has had some previous exposure to matrices. Solultions to the exercises are available in the author's "Matrix Algebra: Exercises and Solutions."