Nonnegative Matrices and Applicable Topics in Linear Algebra

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Publisher : Dover Publications
ISBN 13 : 0486838072
Total Pages : 275 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Nonnegative Matrices and Applicable Topics in Linear Algebra by : Alexander Graham

Download or read book Nonnegative Matrices and Applicable Topics in Linear Algebra written by Alexander Graham and published by Dover Publications. This book was released on 2019-11-13 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonnegative Matrices in the Mathematical Sciences

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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 and Applications

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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.

Totally Nonnegative Matrices

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Publisher : Princeton University Press
ISBN 13 : 0691242410
Total Pages : 264 pages
Book Rating : 4.6/5 (912 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 2022-12-13 with total page 264 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.

Nonnegative Matrices, Positive Operators, And Applications

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Author :
Publisher : World Scientific Publishing Company
ISBN 13 : 981310743X
Total Pages : 362 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Nonnegative Matrices, Positive Operators, And Applications by : Aihui Zhou

Download or read book Nonnegative Matrices, Positive Operators, And Applications written by Aihui Zhou and published by World Scientific Publishing Company. This book was released on 2009-08-24 with total page 362 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.

Linear Algebra and Matrices

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 1470418525
Total Pages : 338 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Linear Algebra and Matrices by : Helene Shapiro

Download or read book Linear Algebra and Matrices written by Helene Shapiro and published by American Mathematical Soc.. This book was released on 2015-10-08 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems. Notable features include a discussion of the Weyr characteristic and Weyr canonical forms, and their relationship to the better-known Jordan canonical form; the use of block cyclic matrices and directed graphs to prove Frobenius's theorem on the structure of the eigenvalues of a nonnegative, irreducible matrix; and the inclusion of such combinatorial topics as BIBDs, Hadamard matrices, and strongly regular graphs. Also included are McCoy's theorem about matrices with property P, the Bruck-Ryser-Chowla theorem on the existence of block designs, and an introduction to Markov chains. This book is intended for those who are familiar with the linear algebra covered in a typical first course and are interested in learning more advanced results.

Nonnegative Matrices in Dynamic Systems

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Author :
Publisher : Wiley-Interscience
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.:/5 (5 download)

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Book Synopsis Nonnegative Matrices in Dynamic Systems by : Abraham Berman

Download or read book Nonnegative Matrices in Dynamic Systems written by Abraham Berman and published by Wiley-Interscience. This book was released on 1989 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Matrix Theory: A Second Course

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Publisher : Springer Science & Business Media
ISBN 13 : 1489904719
Total Pages : 269 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Matrix Theory: A Second Course by : James M. Ortega

Download or read book Matrix Theory: A Second Course written by James M. Ortega and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra and matrix theory are essentially synonymous terms for an area of mathematics that has become one of the most useful and pervasive tools in a wide range of disciplines. It is also a subject of great mathematical beauty. In consequence of both of these facts, linear algebra has increasingly been brought into lower levels of the curriculum, either in conjunction with the calculus or separate from it but at the same level. A large and still growing number of textbooks has been written to satisfy this need, aimed at students at the junior, sophomore, or even freshman levels. Thus, most students now obtaining a bachelor's degree in the sciences or engineering have had some exposure to linear algebra. But rarely, even when solid courses are taken at the junior or senior levels, do these students have an adequate working knowledge of the subject to be useful in graduate work or in research and development activities in government and industry. In particular, most elementary courses stop at the point of canonical forms, so that while the student may have "seen" the Jordan and other canonical forms, there is usually little appreciation of their usefulness. And there is almost never time in the elementary courses to deal with more specialized topics like nonnegative matrices, inertia theorems, and so on. In consequence, many graduate courses in mathematics, applied mathe matics, or applications develop certain parts of matrix theory as needed.

Introduction to Applied Linear Algebra

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Publisher : Cambridge University Press
ISBN 13 : 1316518965
Total Pages : 477 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Introduction to Applied Linear Algebra by : Stephen Boyd

Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Nonnegative Matrices

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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:

Handbook of Linear Algebra, Second Edition

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Publisher : CRC Press
ISBN 13 : 1466507284
Total Pages : 1906 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Handbook of Linear Algebra, Second Edition by : Leslie Hogben

Download or read book Handbook of Linear Algebra, Second Edition written by Leslie Hogben and published by CRC Press. This book was released on 2013-11-26 with total page 1906 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters. New to the Second Edition Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems More chapters on applications of linear algebra, including epidemiology and quantum error correction New chapter on using the free and open source software system Sage for linear algebra Additional sections in the chapters on sign pattern matrices and applications to geometry Conjectures and open problems in most chapters on advanced topics Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.

Matrices

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Publisher : World Scientific
ISBN 13 : 9814667978
Total Pages : 595 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Matrices by : Shmuel Friedland

Download or read book Matrices written by Shmuel Friedland and published by World Scientific. This book was released on 2015-10-29 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume deals with advanced topics in matrix theory using the notions and tools from algebra, analysis, geometry and numerical analysis. It consists of seven chapters that are loosely connected and interdependent. The choice of the topics is very personal and reflects the subjects that the author was actively working on in the last 40 years. Many results appear for the first time in the volume. Readers will encounter various properties of matrices with entries in integral domains, canonical forms for similarity, and notions of analytic, pointwise and rational similarity of matrices with entries which are locally analytic functions in one variable. This volume is also devoted to various properties of operators in inner product space, with tensor products and other concepts in multilinear algebra, and the theory of non-negative matrices. It will be of great use to graduate students and researchers working in pure and applied mathematics, bioinformatics, computer science, engineering, operations research, physics and statistics."--

Linear Algebra and Matrices

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Author :
Publisher : SIAM
ISBN 13 : 1611975131
Total Pages : 301 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Linear Algebra and Matrices by : Shmuel Friedland

Download or read book Linear Algebra and Matrices written by Shmuel Friedland and published by SIAM. This book was released on 2018-01-30 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory textbook grew out of several courses in linear algebra given over more than a decade and includes such helpful material as constructive discussions about the motivation of fundamental concepts, many worked-out problems in each chapter, and topics rarely covered in typical linear algebra textbooks.The authors use abstract notions and arguments to give the complete proof of the Jordan canonical form and, more generally, the rational canonical form of square matrices over fields. They also provide the notion of tensor products of vector spaces and linear transformations. Matrices are treated in depth, with coverage of the stability of matrix iterations, the eigenvalue properties of linear transformations in inner product spaces, singular value decomposition, and min-max characterizations of Hermitian matrices and nonnegative irreducible matrices. The authors show the many topics and tools encompassed by modern linear algebra to emphasize its relationship to other areas of mathematics. The text is intended for advanced undergraduate students. Beginning graduate students seeking an introduction to the subject will also find it of interest.

Nonnegative Matrix Factorization

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Author :
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.

Matrix Algebra: Exercises and Solutions

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Publisher : Springer Science & Business Media
ISBN 13 : 1461301815
Total Pages : 292 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Matrix Algebra: Exercises and Solutions by : David A. Harville

Download or read book Matrix Algebra: Exercises and Solutions written by David A. Harville and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains over 300 exercises and solutions that together cover a wide variety of topics in matrix algebra. They can be used for independent study or in creating a challenging and stimulating environment that encourages active engagement in the learning process. The requisite background is some previous exposure to matrix algebra of the kind obtained in a first course. The exercises are those from an earlier book by the same author entitled Matrix Algebra From a Statistician's Perspective. They have been restated (as necessary) to stand alone, and the book includes extensive and detailed summaries of all relevant terminology and notation. The coverage includes topics of special interest and relevance in statistics and related disciplines, as well as standard topics. The overlap with exercises available from other sources is relatively small. This collection of exercises and their solutions will be a useful reference for students and researchers in matrix algebra. It will be of interest to mathematicians and statisticians.

Linear Algebra in Action

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Author :
Publisher : American Mathematical Society
ISBN 13 : 1470472066
Total Pages : 512 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Linear Algebra in Action by : Harry Dym

Download or read book Linear Algebra in Action written by Harry Dym and published by American Mathematical Society. This book was released on 2023-07-18 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based largely on courses that the author taught at the Feinberg Graduate School of the Weizmann Institute. It conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that the author has found to be useful in his own research and wishes that he had been exposed to as a graduate student. Roughly the first quarter of the book reviews the contents of a basic course in linear algebra, plus a little. The remaining chapters treat singular value decompositions, convexity, special classes of matrices, projections, assorted algorithms, and a number of applications. The applications are drawn from vector calculus, numerical analysis, control theory, complex analysis, convex optimization, and functional analysis. In particular, fixed point theorems, extremal problems, best approximations, matrix equations, zero location and eigenvalue location problems, matrices with nonnegative entries, and reproducing kernels are discussed. This new edition differs significantly from the second edition in both content and style. It includes a number of topics that did not appear in the earlier edition and excludes some that did. Moreover, most of the material that has been adapted from the earlier edition has been extensively rewritten and reorganized.

Linear Algebra and Matrices

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Author :
Publisher : SIAM
ISBN 13 : 161197514X
Total Pages : 301 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Linear Algebra and Matrices by : Shmuel Friedland

Download or read book Linear Algebra and Matrices written by Shmuel Friedland and published by SIAM. This book was released on 2018-01-30 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory textbook grew out of several courses in linear algebra given over more than a decade and includes such helpful material as constructive discussions about the motivation of fundamental concepts, many worked-out problems in each chapter, and topics rarely covered in typical linear algebra textbooks.The authors use abstract notions and arguments to give the complete proof of the Jordan canonical form and, more generally, the rational canonical form of square matrices over fields. They also provide the notion of tensor products of vector spaces and linear transformations. Matrices are treated in depth, with coverage of the stability of matrix iterations, the eigenvalue properties of linear transformations in inner product spaces, singular value decomposition, and min-max characterizations of Hermitian matrices and nonnegative irreducible matrices. The authors show the many topics and tools encompassed by modern linear algebra to emphasize its relationship to other areas of mathematics. The text is intended for advanced undergraduate students. Beginning graduate students seeking an introduction to the subject will also find it of interest.