Nonnegative Matrices And Applications

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Nonnegative Matrices and Applications

Author : R. B. Bapat
Publisher : Cambridge University Press
ISBN 13 : 0521571677
Total Pages : 351 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis Nonnegative Matrices and Applications by : R. B. Bapat

Download or read book Nonnegative Matrices and Applications written by R. B. Bapat and published by Cambridge University Press. This book was released on 1997-03-28 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 in the Mathematical Sciences

Author : Abraham Berman
Publisher : Academic Press
ISBN 13 : 1483260860
Total Pages : 337 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Nonnegative Matrices in the Mathematical Sciences by : Abraham Berman

Download or read book Nonnegative Matrices in the Mathematical Sciences written by Abraham Berman and published by Academic Press. This book was released on 2014-05-10 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Jiu Ding
Publisher : World Scientific Publishing Company
ISBN 13 : 981310743X
Total Pages : 364 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Nonnegative Matrices, Positive Operators, and Applications by : Jiu Ding

Download or read book Nonnegative Matrices, Positive Operators, and Applications written by Jiu Ding and published by World Scientific Publishing Company. This book was released on 2009-08-24 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Totally Nonnegative Matrices

Author : Shaun M. Fallat
Publisher : Princeton University Press
ISBN 13 : 1400839017
Total Pages : 265 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Totally Nonnegative Matrices by : Shaun M. Fallat

Download or read book Totally Nonnegative Matrices written by Shaun M. Fallat and published by Princeton University Press. This book was released on 2011-04-11 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Applications of the Theory of Matrices

Author : F. R. Gantmacher
Publisher : Courier Corporation
ISBN 13 : 0486445542
Total Pages : 336 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Applications of the Theory of Matrices by : F. R. Gantmacher

Download or read book Applications of the Theory of Matrices written by F. R. Gantmacher and published by Courier Corporation. This book was released on 2005-01-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The breadth of matrix theory's applications is reflected by this volume, which features material of interest to applied mathematicians as well as to control engineers studying stability of a servo-mechanism and numerical analysts evaluating the roots of a polynomial. Starting with a survey of complex symmetric, antisymmetric, and orthogonal matrices, the text advances to explorations of singular bundles of matrices and matrices with nonnegative elements. Applied mathematicians will take particular note of the full and readable chapter on applications of matrix theory to the study of systems of linear differential equations, and the text concludes with an exposition on the Routh-Hurwitz problem plus several helpful appendixes. 1959 edition.

Nonnegative Matrices

Author : Henryk Minc
Publisher :
ISBN 13 :
Total Pages : 226 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Nonnegative Matrices by : Henryk Minc

Download or read book Nonnegative Matrices written by Henryk Minc and published by . This book was released on 1974 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Non-negative Matrices and Markov Chains

Author : E. Seneta
Publisher : Springer Science & Business Media
ISBN 13 : 0387327924
Total Pages : 295 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Non-negative Matrices and Markov Chains by : E. Seneta

Download or read book Non-negative Matrices and Markov Chains written by E. Seneta and published by Springer Science & Business Media. This book was released on 2006-07-02 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Matrix Algebra and Its Applications to Statistics and Econometrics

Author : Calyampudi Radhakrishna Rao
Publisher : World Scientific
ISBN 13 : 9789810232689
Total Pages : 560 pages
Book Rating : 4.2/5 (326 download)

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Book Synopsis Matrix Algebra and Its Applications to Statistics and Econometrics by : Calyampudi Radhakrishna Rao

Download or read book Matrix Algebra and Its Applications to Statistics and Econometrics written by Calyampudi Radhakrishna Rao and published by World Scientific. This book was released on 1998 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: "I recommend this book for its extensive coverage of topics not easily found elsewhere and for its focus on applications".Zentralblatt MATH"The book is an excellent source on linear algebra, matrix theory and applications in statistics and econometrics, and is unique in many ways. I recommend it to anyone interested in these disciplines, and especially in how they benefit from one another".Statistical Papers, 2000

A Combinatorial Approach to Matrix Theory and Its Applications

Author : Richard A. Brualdi
Publisher : CRC Press
ISBN 13 : 9781420082241
Total Pages : 288 pages
Book Rating : 4.0/5 (822 download)

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Book Synopsis A Combinatorial Approach to Matrix Theory and Its Applications by : Richard A. Brualdi

Download or read book A Combinatorial Approach to Matrix Theory and Its Applications written by Richard A. Brualdi and published by CRC Press. This book was released on 2008-08-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike most elementary books on matrices, A Combinatorial Approach to Matrix Theory and Its Applications employs combinatorial and graph-theoretical tools to develop basic theorems of matrix theory, shedding new light on the subject by exploring the connections of these tools to matrices. After reviewing the basics of graph theory, elementary counting formulas, fields, and vector spaces, the book explains the algebra of matrices and uses the König digraph to carry out simple matrix operations. It then discusses matrix powers, provides a graph-theoretical definition of the determinant using the Coates digraph of a matrix, and presents a graph-theoretical interpretation of matrix inverses. The authors develop the elementary theory of solutions of systems of linear equations and show how to use the Coates digraph to solve a linear system. They also explore the eigenvalues, eigenvectors, and characteristic polynomial of a matrix; examine the important properties of nonnegative matrices that are part of the Perron–Frobenius theory; and study eigenvalue inclusion regions and sign-nonsingular matrices. The final chapter presents applications to electrical engineering, physics, and chemistry. Using combinatorial and graph-theoretical tools, this book enables a solid understanding of the fundamentals of matrix theory and its application to scientific areas.

Matrices

Author : Denis Serre
Publisher : Springer Science & Business Media
ISBN 13 : 1441976833
Total Pages : 291 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Matrices by : Denis Serre

Download or read book Matrices written by Denis Serre and published by Springer Science & Business Media. This book was released on 2010-10-26 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the École Normale Supérieure de Lyon.

Nonnegative Matrix Factorization

Author : Nicolas Gillis
Publisher : SIAM
ISBN 13 : 1611976413
Total Pages : 376 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Nonnegative Matrix Factorization by : Nicolas Gillis

Download or read book Nonnegative Matrix Factorization written by Nicolas Gillis and published by SIAM. This book was released on 2020-12-18 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonnegative Matrices, Positive Operators, and Applications

Author : Jiu Ding
Publisher :
ISBN 13 : 9789812839183
Total Pages : pages
Book Rating : 4.8/5 (391 download)

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Book Synopsis Nonnegative Matrices, Positive Operators, and Applications by : Jiu Ding

Download or read book Nonnegative Matrices, Positive Operators, and Applications written by Jiu Ding and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonnegative Matrix and Tensor Factorizations

Author : Andrzej Cichocki
Publisher : John Wiley & Sons
ISBN 13 : 9780470747285
Total Pages : 500 pages
Book Rating : 4.7/5 (472 download)

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Book Synopsis Nonnegative Matrix and Tensor Factorizations by : Andrzej Cichocki

Download or read book Nonnegative Matrix and Tensor Factorizations written by Andrzej Cichocki and published by John Wiley & Sons. This book was released on 2009-07-10 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad survey of models and efficient algorithms for Nonnegative Matrix Factorization (NMF). This includes NMF’s various extensions and modifications, especially Nonnegative Tensor Factorizations (NTF) and Nonnegative Tucker Decompositions (NTD). NMF/NTF and their extensions are increasingly used as tools in signal and image processing, and data analysis, having garnered interest due to their capability to provide new insights and relevant information about the complex latent relationships in experimental data sets. It is suggested that NMF can provide meaningful components with physical interpretations; for example, in bioinformatics, NMF and its extensions have been successfully applied to gene expression, sequence analysis, the functional characterization of genes, clustering and text mining. As such, the authors focus on the algorithms that are most useful in practice, looking at the fastest, most robust, and suitable for large-scale models. Key features: Acts as a single source reference guide to NMF, collating information that is widely dispersed in current literature, including the authors’ own recently developed techniques in the subject area. Uses generalized cost functions such as Bregman, Alpha and Beta divergences, to present practical implementations of several types of robust algorithms, in particular Multiplicative, Alternating Least Squares, Projected Gradient and Quasi Newton algorithms. Provides a comparative analysis of the different methods in order to identify approximation error and complexity. Includes pseudo codes and optimized MATLAB source codes for almost all algorithms presented in the book. The increasing interest in nonnegative matrix and tensor factorizations, as well as decompositions and sparse representation of data, will ensure that this book is essential reading for engineers, scientists, researchers, industry practitioners and graduate students across signal and image processing; neuroscience; data mining and data analysis; computer science; bioinformatics; speech processing; biomedical engineering; and multimedia.

Matrix Theory and Applications

Author : Charles R. Johnson
Publisher : American Mathematical Soc.
ISBN 13 : 0821801546
Total Pages : 272 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Matrix Theory and Applications by : Charles R. Johnson

Download or read book Matrix Theory and Applications written by Charles R. Johnson and published by American Mathematical Soc.. This book was released on 1990 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the lecture notes prepared for the AMS Short Course on Matrix Theory and Applications, held in Phoenix in January, 1989. Matrix theory continues to enjoy a renaissance that has accelerated in the past decade, in part because of stimulation from a variety of applications and considerable interplay with other parts of mathematics. In addition, the great increase in the number and vitality of specialists in the field has dispelled the popular misconception that the subject has been fully researched.

Positive Operator Semigroups

Author : András Bátkai
Publisher : Birkhäuser
ISBN 13 : 3319428136
Total Pages : 364 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Positive Operator Semigroups by : András Bátkai

Download or read book Positive Operator Semigroups written by András Bátkai and published by Birkhäuser. This book was released on 2017-02-13 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications. Positivity is a property which naturally appears in physical, chemical, biological or economic processes. It adds a beautiful and far reaching mathematical structure to the dynamical systems and operators describing these processes. In the first part, the finite dimensional theory in a coordinate-free way is developed, which is difficult to find in literature. This is a good opportunity to present the main ideas of the Perron-Frobenius theory in a way which can be used in the infinite dimensional situation. Applications to graph matrices, age structured population models and economic models are discussed. The infinite dimensional theory of positive operator semigroups with their spectral and asymptotic theory is developed in the second part. Recent applications illustrate the theory, like population equations, neutron transport theory, delay equations or flows in networks. Each chapter is accompanied by a large set of exercises. An up-to-date bibliography and a detailed subject index help the interested reader. The book is intended primarily for graduate and master students. The finite dimensional part, however, can be followed by an advanced bachelor with a solid knowledge of linear algebra and calculus.

Special Matrices and Their Applications in Numerical Mathematics

Author : Miroslav Fiedler
Publisher : Courier Corporation
ISBN 13 : 0486783480
Total Pages : 384 pages
Book Rating : 4.4/5 (867 download)

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Book Synopsis Special Matrices and Their Applications in Numerical Mathematics by : Miroslav Fiedler

Download or read book Special Matrices and Their Applications in Numerical Mathematics written by Miroslav Fiedler and published by Courier Corporation. This book was released on 2013-12-01 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and corrected second edition of a classic on special matrices provides researchers in numerical linear algebra and students of general computational mathematics with an essential reference. 1986 edition.

Matrices in Combinatorics and Graph Theory

Author : Bolian Liu
Publisher : Springer Science & Business Media
ISBN 13 : 9780792364696
Total Pages : 326 pages
Book Rating : 4.3/5 (646 download)

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Book Synopsis Matrices in Combinatorics and Graph Theory by : Bolian Liu

Download or read book Matrices in Combinatorics and Graph Theory written by Bolian Liu and published by Springer Science & Business Media. This book was released on 2000-10-31 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics and Matrix Theory have a symbiotic, or mutually beneficial, relationship. This relationship is discussed in my paper The symbiotic relationship of combinatorics and matrix theoryl where I attempted to justify this description. One could say that a more detailed justification was given in my book with H. J. Ryser entitled Combinatorial Matrix Theon? where an attempt was made to give a broad picture of the use of combinatorial ideas in matrix theory and the use of matrix theory in proving theorems which, at least on the surface, are combinatorial in nature. In the book by Liu and Lai, this picture is enlarged and expanded to include recent developments and contributions of Chinese mathematicians, many of which have not been readily available to those of us who are unfamiliar with Chinese journals. Necessarily, there is some overlap with the book Combinatorial Matrix Theory. Some of the additional topics include: spectra of graphs, eulerian graph problems, Shannon capacity, generalized inverses of Boolean matrices, matrix rearrangements, and matrix completions. A topic to which many Chinese mathematicians have made substantial contributions is the combinatorial analysis of powers of nonnegative matrices, and a large chapter is devoted to this topic. This book should be a valuable resource for mathematicians working in the area of combinatorial matrix theory. Richard A. Brualdi University of Wisconsin - Madison 1 Linear Alg. Applies., vols. 162-4, 1992, 65-105 2Camhridge University Press, 1991.