Algebraic Properties Of Generalized Inverses

DOWNLOAD

Download Algebraic Properties Of Generalized Inverses PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Algebraic Properties Of Generalized Inverses book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Algebraic Properties Of Generalized Inverses

DOWNLOAD
Author : Dragana S. Cvetković‐Ilić
language : en
Publisher: Springer
Release Date : 2017-10-07

Algebraic Properties Of Generalized Inverses written by Dragana S. Cvetković‐Ilić and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-07 with Mathematics categories.

This book addresses selected topics in the theory of generalized inverses. Following a discussion of the “reverse order law” problem and certain problems involving completions of operator matrices, it subsequently presents a specific approach to solving the problem of the reverse order law for {1} -generalized inverses. Particular emphasis is placed on the existence of Drazin invertible completions of an upper triangular operator matrix; on the invertibility and different types of generalized invertibility of a linear combination of operators on Hilbert spaces and Banach algebra elements; on the problem of finding representations of the Drazin inverse of a 2x2 block matrix; and on selected additive results and algebraic properties for the Drazin inverse. In addition to the clarity of its content, the book discusses the relevant open problems for each topic discussed. Comments on the latest references on generalized inverses are also included. Accordingly, the book will be useful for graduate students, PhD students and researchers, but also for a broader readership interested in these topics.

Generalized Inverses

DOWNLOAD
Author : Adi Ben-Israel
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18

Generalized Inverses written by Adi Ben-Israel 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 2006-04-18 with Mathematics categories.

This second edition accounts for many major developments in generalized inverses while maintaining the informal and leisurely style of the 1974 first edition. Added material includes a chapter on applications, new exercises, and an appendix on the work of E.H. Moore.

Algebraic Theory Of Generalized Inverses

DOWNLOAD
Author : Jianlong Chen
language : en
Publisher: Springer Nature
Release Date : 2024-02-28

Algebraic Theory Of Generalized Inverses written by Jianlong Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-28 with Mathematics categories.

Most of the existing monographs on generalized inverses are based on linear algebra tools and geometric methods of Banach (Hilbert) spaces to introduce generalized inverses of complex matrices and operators and their related applications, or focus on generalized inverses of matrices over special rings like division rings and integral domains, and does not include the results in general algebraic structures such as arbitrary rings, semigroups and categories, which are precisely the most general cases. In this book, five important generalized inverses are introduced in these algebraic structures. Moreover, noting that the (pseudo) core inverse was introduced in the last decade and has attracted much attention, this book also covers the very rich research results on it, so as to be a necessary supplement to the existing monographs. This book starts with decompositions of matrices, introduces the basic properties of generalized inverses of matrices, and then discusses generalizedinverses of elements in rings and semigroups, as well as morphisms in categories. The algebraic nature of generalized inverses is presented, and the behavior of generalized inverses are related to the properties of the algebraic system. Scholars and graduate students working on the theory of rings, semigroups and generalized inverses of matrices and operators will find this book helpful.

Matrix And Operator Equations And Applications

DOWNLOAD
Author : Mohammad Sal Moslehian
language : en
Publisher: Springer Nature
Release Date : 2023-07-29

Matrix And Operator Equations And Applications written by Mohammad Sal Moslehian and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-29 with Mathematics categories.

This book concerns matrix and operator equations that are widely applied in various disciplines of science to formulate challenging problems and solve them in a faithful way. The main aim of this contributed book is to study several important matrix and operator equalities and equations in a systematic and self-contained fashion. Some powerful methods have been used to investigate some significant equations in functional analysis, operator theory, matrix analysis, and numerous subjects in the last decades. The book is divided into two parts: (I) Matrix Equations and (II) Operator Equations. In the first part, the state-of-the-art of systems of matrix equations is given and generalized inverses are used to find their solutions. The semi-tensor product of matrices is used to solve quaternion matrix equations. The contents of some chapters are related to the relationship between matrix inequalities, matrix means, numerical range, and matrix equations. In addition, quaternion algebras and their applications are employed in solving some famous matrix equations like Sylvester, Stein, and Lyapunov equations. A chapter devoted to studying Hermitian polynomial matrix equations, which frequently arise from linear-quadratic control problems. Moreover, some classical and recently discovered inequalities for matrix exponentials are reviewed. In the second part, the latest developments in solving several equations appearing in modern operator theory are demonstrated. These are of interest to a wide audience of pure and applied mathematicians. For example, the Daugavet equation in the linear and nonlinear setting, iterative processes and Volterra-Fredholm integral equations, semicircular elements induced by connected finite graphs, free probability, singular integral operators with shifts, and operator differential equations closely related to the properties of the coefficient operators in some equations are discussed. The chapters give a comprehensive account of their subjects. The exhibited chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.

Matrix Algebra From A Statistician S Perspective

DOWNLOAD
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."

Matrix Algebra

DOWNLOAD
Author : James E. Gentle
language : en
Publisher: Springer
Release Date : 2017-10-12

Matrix Algebra written by James E. Gentle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-12 with Mathematics categories.

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.

Applied Matrix Algebra In The Statistical Sciences

DOWNLOAD
Author : Alexander Basilevsky
language : en
Publisher: Courier Corporation
Release Date : 2005-12-27

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 2005-12-27 with Mathematics categories.

This comprehensive text covers both applied and theoretical branches of matrix algebra in the statistical sciences. It also provides a bridge between linear algebra and statistical models. Appropriate for advanced undergraduate and graduate students, the self-contained treatment also constitutes a handy reference for researchers. The only mathematical background necessary is a sound knowledge of high school mathematics and a first course in statistics. Consisting of two interrelated parts, this volume begins with the basic structure of vectors and vector spaces. The latter part emphasizes the diverse properties of matrices and their associated linear transformations--and how these, in turn, depend upon results derived from linear vector spaces. An overview of introductory concepts leads to more advanced topics such as latent roots and vectors, generalized inverses, and nonnegative matrices. Each chapter concludes with a section on real-world statistical applications, plus exercises that offer concrete examples of the applications of matrix algebra.

Generalized Inverses And Applications

DOWNLOAD
Author : M. Zuhair Nashed
language : en
Publisher: Elsevier
Release Date : 2014-05-10

Generalized Inverses And Applications written by M. Zuhair Nashed and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

Generalized Inverses and Applications, contains the proceedings of an Advanced Seminar on Generalized Inverses and Applications held at the University of Wisconsin-Madison on October 8-10, 1973 under the auspices of the university's Mathematics Research Center. The seminar provided a forum for discussing the basic theory of generalized inverses and their applications to analysis and operator equations. Numerical analysis and approximation methods are considered, along with applications to statistics and econometrics, optimization, system theory, and operations research. Comprised of 14 chapters, this book begins by describing a unified approach to generalized inverses of linear operators, with particular reference to algebraic, topological, extremal, and proximinal properties. The reader is then introduced to the algebraic aspects of the generalized inverse of a rectangular matrix; the Fredholm pseudoinverse; and perturbations and approximations for generalized inverses and linear operator equations. Subsequent chapters deal with various applications of generalized inverses, including programming, games, and networks, as well as estimation and aggregation in econometrics. This monograph will be of interest to mathematicians and students of mathematics.

Advanced Techniques With Block Matrices Of Operators

DOWNLOAD
Author : Mohammad Sal Moslehian
language : en
Publisher: Springer Nature
Release Date : 2024-08-28

Advanced Techniques With Block Matrices Of Operators written by Mohammad Sal Moslehian and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-28 with Mathematics categories.

This book introduces several powerful techniques and fundamental ideas involving block matrices of operators, as well as matrices with elements in a C*-algebra. These techniques allow for the solution of problems that may be difficult to treat. Specifically, 2×2 operator matrices yield significant mathematical inequalities in various fields of operator theory and matrix analysis. The authors employ block matrices to simplify complicated problems. Operator matrices have garnered attention for their applications in quantum information and computing theories. Each chapter concludes with a diverse set of exercises and problems for readers, along with references to relevant literature. Some problems pose open questions, while others challenge readers and provide suggestions for future research. This book is suitable for an advanced undergraduate or graduate course and can be used in the classroom. It also serves as a valuable resource for researchers and students in mathematics and physics who have a basic understanding of linear algebra, functional analysis, and operator theory.

Matrix Algebra For Linear Models

DOWNLOAD
Author : Marvin H. J. Gruber
language : en
Publisher: John Wiley & Sons
Release Date : 2013-12-31

Matrix Algebra For Linear Models written by Marvin H. J. Gruber and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-31 with Mathematics categories.

A self-contained introduction to matrix analysis theory and applications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Models offers a succinct summary of matrix theory and its related applications to statistics, especially linear models. The book provides a unified presentation of the mathematical properties and statistical applications of matrices in order to define and manipulate data. Written for theoretical and applied statisticians, the book utilizes multiple numerical examples to illustrate key ideas, methods, and techniques crucial to understanding matrix algebra’s application in linear models. Matrix Algebra for Linear Models expertly balances concepts and methods allowing for a side-by-side presentation of matrix theory and its linear model applications. Including concise summaries on each topic, the book also features: Methods of deriving results from the properties of eigenvalues and the singular value decomposition Solutions to matrix optimization problems for obtaining more efficient biased estimators for parameters in linear regression models A section on the generalized singular value decomposition Multiple chapter exercises with selected answers to enhance understanding of the presented material Matrix Algebra for Linear Models is an ideal textbook for advanced undergraduate and graduate-level courses on statistics, matrices, and linear algebra. The book is also an excellent reference for statisticians, engineers, economists, and readers interested in the linear statistical model.