Nonnegative Matrices Positive Operators And Applications PDF Download
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Author | : Jiu Ding |
Publisher | : World Scientific Publishing Company |
Total Pages | : 364 |
Release | : 2009-08-24 |
Genre | : Mathematics |
ISBN | : 981310743X |
Download Nonnegative Matrices, Positive Operators, and Applications Book in PDF, ePub and Kindle
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.
Author | : Jiu Ding |
Publisher | : |
Total Pages | : |
Release | : 2009 |
Genre | : |
ISBN | : 9789812839183 |
Download Nonnegative Matrices, Positive Operators, and Applications Book in PDF, ePub and Kindle
Author | : R. B. Bapat |
Publisher | : Cambridge University Press |
Total Pages | : 351 |
Release | : 1997-03-28 |
Genre | : Mathematics |
ISBN | : 0521571677 |
Download Nonnegative Matrices and Applications Book in PDF, ePub and Kindle
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.
Author | : Abraham Berman |
Publisher | : Academic Press |
Total Pages | : 337 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483260860 |
Download Nonnegative Matrices in the Mathematical Sciences Book in PDF, ePub and Kindle
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.
Author | : Eugene Seneta |
Publisher | : John Wiley & Sons |
Total Pages | : 234 |
Release | : 1973 |
Genre | : Mathematics |
ISBN | : |
Download Non-negative Matrices Book in PDF, ePub and Kindle
Author | : Shaun M. Fallat |
Publisher | : Princeton University Press |
Total Pages | : 264 |
Release | : 2022-12-13 |
Genre | : Mathematics |
ISBN | : 0691242410 |
Download Totally Nonnegative Matrices Book in PDF, ePub and Kindle
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.
Author | : Alexander Graham |
Publisher | : |
Total Pages | : 280 |
Release | : 1987 |
Genre | : Mathematics |
ISBN | : |
Download Nonnegative Matrices and Applicable Topics in Linear Algebra Book in PDF, ePub and Kindle
Author | : András Bátkai |
Publisher | : Birkhäuser |
Total Pages | : 364 |
Release | : 2017-02-13 |
Genre | : Mathematics |
ISBN | : 3319428136 |
Download Positive Operator Semigroups Book in PDF, ePub and Kindle
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.
Author | : Abraham Berman |
Publisher | : World Scientific |
Total Pages | : 218 |
Release | : 2003-04-11 |
Genre | : Mathematics |
ISBN | : 9814486000 |
Download Completely Positive Matrices Book in PDF, ePub and Kindle
A real matrix is positive semidefinite if it can be decomposed as A=BB′. 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=BB′ 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.
Author | : Henryk Minc |
Publisher | : |
Total Pages | : 226 |
Release | : 1974 |
Genre | : Matrices |
ISBN | : |
Download Nonnegative Matrices Book in PDF, ePub and Kindle