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 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.
Nonnegative Matrices Positive Operators And Applications
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Author : Aihui Zhou
language : en
Publisher: World Scientific Publishing Company
Release Date : 2009-08-24
Nonnegative Matrices Positive Operators And Applications written by Aihui Zhou 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.
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.
Totally Nonnegative Matrices
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Author : Shaun M. Fallat
language : en
Publisher: Princeton University Press
Release Date : 2011-04-11
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 2011-04-11 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.
Completely Positive Matrices
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Author : Abraham Berman
language : en
Publisher: World Scientific
Release Date : 2003
Completely Positive Matrices written by Abraham Berman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
A real matrix is positive semidefinite if it can be decomposed as A = BBOC . In some applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A = BBOC is known as the cp- rank of A . This invaluable book focuses on necessary conditions and sufficient conditions for complete positivity, as well as bounds for the cp- rank. The methods are combinatorial, geometric and algebraic. The required background on nonnegative matrices, cones, graphs and Schur complements is outlined. Contents: Preliminaries: Matrix Theoretic Background; Positive Semidefinite Matrices; Nonnegative Matrices and M -Matrices; Schur Complements; Graphs; Convex Cones; The PSD Completion Problem; Complete Positivity: Definition and Basic Properties; Cones of Completely Positive Matrices; Small Matrices; Complete Positivity and the Comparison Matrix; Completely Positive Graphs; Completely Positive Matrices Whose Graphs are Not Completely Positive; Square Factorizations; Functions of Completely Positive Matrices; The CP Completion Problem; CP Rank: Definition and Basic Results; Completely Positive Matrices of a Given Rank; Completely Positive Matrices of a Given Order; When is the CP-Rank Equal to the Rank?. Readership: Upper level undergraduates, graduate students, academics and researchers interested in matrix theory."
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 is the softcover reprint of a very popular hardcover edition, a revised version of the first edition, originally published by Prentice Hall in 1962 and regarded as a classic in its field. In some places, newer research results, e.g. results on weak regular splittings, have been incorporated in the revision, and in other places, new material has been added in the chapters, as well as at the end of chapters, in the form of additional up-to-date references and some recent theorems to give the reader some newer directions to pursue. The material in the new chapters is basically self-contained and more exercises have been provided for the readers. While the original version was more linear algebra oriented, the revision attempts to emphasize tools from other areas, such as approximation theory and conformal mapping theory, to access newer results of interest. The book should be of great interest to researchers and graduate students in the field of numerical analysis.
Applied Matrix Algebra In The Statistical Sciences
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Author : Alexander Basilevsky
language : en
Publisher: Courier Corporation
Release Date : 2013-01-18
Applied Matrix Algebra In The Statistical Sciences written by Alexander Basilevsky and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-18 with Mathematics categories.
This comprehensive text offers teachings relevant to both applied and theoretical branches of matrix algebra and provides a bridge between linear algebra and statistical models. Appropriate for advanced undergraduate and graduate students. 1983 edition.
Matrix Methods
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Author : Vadim Olshevsky
language : en
Publisher: World Scientific
Release Date : 2010
Matrix Methods written by Vadim Olshevsky and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applications usually live as if in three separate worlds. In this volume, maybe for the first time ever, they are compiled together as one entity as it was at the Moscow meeting, where the algebraic part was impersonated by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk. All topics intervened in plenary sessions are specially categorized into three sections of this volume. --
Nonnegative Matrix Factorization
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Author : Nicolas Gillis
language : en
Publisher: SIAM
Release Date : 2020-12-18
Nonnegative Matrix Factorization written by Nicolas Gillis and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-18 with Mathematics categories.
Nonnegative matrix factorization (NMF) in its modern form has become a standard tool in the analysis of high-dimensional data sets. This book provides a comprehensive and up-to-date account of the most important aspects of the NMF problem and is the first to detail its theoretical aspects, including geometric interpretation, nonnegative rank, complexity, and uniqueness. It explains why understanding these theoretical insights is key to using this computational tool effectively and meaningfully. Nonnegative Matrix Factorization is accessible to a wide audience and is ideal for anyone interested in the workings of NMF. It discusses some new results on the nonnegative rank and the identifiability of NMF and makes available MATLAB codes for readers to run the numerical examples presented in the book. Graduate students starting to work on NMF and researchers interested in better understanding the NMF problem and how they can use it will find this book useful. It can be used in advanced undergraduate and graduate-level courses on numerical linear algebra and on advanced topics in numerical linear algebra and requires only a basic knowledge of linear algebra and optimization.