Algebraic Properties Of Generalized Inverses

Author : Dragana S. Cvetković‐Ilić,Yimin Wei
Publisher : Springer
Page : 194 pages
File Size : 51,7 Mb
Release : 2017-10-07
Category : Mathematics
ISBN : 9789811063497

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Algebraic Properties of Generalized Inverses by Dragana S. Cvetković‐Ilić,Yimin Wei Pdf

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.

Author : Dragana S. Cvetković Ilić
Publisher : Unknown
Page : 128 pages
File Size : 53,6 Mb
Release : 2017
Category : Linear operators
ISBN : 9811063508

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Algebraic Properties of Generalized Inverses by Dragana S. Cvetković Ilić Pdf

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.--

Author : Jianlong Chen
Publisher : Springer Nature
Page : 331 pages
File Size : 45,9 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9789819982851

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Algebraic Theory of Generalized Inverses by Jianlong Chen Pdf

Author : Stephen L. Campbell,Carl D. Meyer
Publisher : SIAM
Page : 289 pages
File Size : 44,9 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 9780898719048

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Generalized Inverses of Linear Transformations by Stephen L. Campbell,Carl D. Meyer Pdf

Generalized (or pseudo-) inverse concepts routinely appear throughout applied mathematics and engineering, in both research literature and textbooks. Although the basic properties are readily available, some of the more subtle aspects and difficult details of the subject are not well documented or understood. First published in 1979, Generalized Inverses of Linear Transformations remains up-to-date and readable, and it includes chapters on Markov chains and the Drazin inverse methods that have become significant to many problems in applied mathematics. The book provides comprehensive coverage of the mathematical theory of generalized inverses coupled with a wide range of important and practical applications that includes topics in electrical and computer engineering, control and optimization, computing and numerical analysis, statistical estimation, and stochastic processes. Audience: intended for use as a reference by applied scientists and engineers.

Author : Adi Ben-Israel,Thomas N.E. Greville
Publisher : Springer Science & Business Media
Page : 420 pages
File Size : 49,9 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387216348

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Generalized Inverses by Adi Ben-Israel,Thomas N.E. Greville Pdf

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.

Author : Guorong Wang,Yimin Wei,Sanzheng Qiao
Publisher : Springer
Page : 378 pages
File Size : 53,6 Mb
Release : 2018-05-12
Category : Mathematics
ISBN : 9789811301469

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Generalized Inverses: Theory and Computations by Guorong Wang,Yimin Wei,Sanzheng Qiao Pdf

This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics. It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.

Author : M. Zuhair Nashed
Publisher : Elsevier
Page : 1069 pages
File Size : 44,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483270296

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Generalized Inverses and Applications by M. Zuhair Nashed Pdf

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.

Author : Calyampudi Radhakrishna Rao,Sujit Kumar Mitra
Publisher : John Wiley & Sons
Page : 264 pages
File Size : 55,9 Mb
Release : 1971
Category : Mathematics
ISBN : MINN:31951000012834C

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Generalized Inverse of Matrices and Its Applications by Calyampudi Radhakrishna Rao,Sujit Kumar Mitra Pdf

Notations and preliminaries; Generalized inverse of a matrix; Three basic types of g-inverses; Other special types of g-inverse; Projectors, idempotent matrices and partial isometry; Simulatneous reduction of a pair of herminitian forms; Estimation of parameters in linear models; Conditions for optimality and validity of least-squares theory; Distribution of quadratic forms; Miscellaneous applications of g-inverses; Computational methods; Bibliography on generalized inverses and applications; Index.

Author : Yimin Wei,Predrag Stanimirovic,Marko Petkovic
Publisher : World Scientific
Page : 472 pages
File Size : 45,7 Mb
Release : 2018-07-18
Category : Mathematics
ISBN : 9789813238688

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Numerical And Symbolic Computations Of Generalized Inverses by Yimin Wei,Predrag Stanimirovic,Marko Petkovic Pdf

We introduce new methods connecting numerics and symbolic computations, i.e., both the direct and iterative methods as well as the symbolic method for computing the generalized inverses. These will be useful for Engineers and Statisticians, in addition to applied mathematicians.Also, main applications of generalized inverses will be presented. Symbolic method covered in our book but not discussed in other book, which is important for numerical-symbolic computations.

Author : Ivan Kyrchei
Publisher : Unknown
Page : 128 pages
File Size : 40,8 Mb
Release : 2021-12-31
Category : Electronic
ISBN : 1685073565

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Generalized Inverses: Algorithms and Applications by Ivan Kyrchei Pdf

Generalized Inverses: Algorithms and Applications demonstrates some of the latest hot topics on generalized inverse matrices and their applications. Each article has been carefully selected to present substantial research results. Topics discussed herein include recent advances in exploring of generalizations of the core inverse, particularly in composing appropriate outer inverses and the Moore-Penrose inverse such as OMP, MPO and MPOMP inverses; in analyzing of properties of the BT inverse and the BT-order; in perturbation estimations for the Drazin inverse; in using generalized inverses to solve systems of quaternion matrix equations and Sylvester-type tensor equations under t-product; in computing and approximating the matrix generalized inverses by hyperpower family of iterative methods of arbitrary convergence order; and in studying of the weighted pseudoinverse matrices with singular indefinite weights.

Author : K.P.S. Bhaskara Rao
Publisher : CRC Press
Page : 192 pages
File Size : 47,7 Mb
Release : 2002-03-21
Category : Mathematics
ISBN : 9780203218877

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Theory of Generalized Inverses Over Commutative Rings by K.P.S. Bhaskara Rao Pdf

The theory of generalized inverses of real or complex matrices has been expertly developed and documented. But the generalized inverses of matrices over rings have received comprehensive treatment only recently. In this book, the author, who contributed to the research and development of the theory, explains his results. He explores regular element

Author : James E. Gentle
Publisher : Springer
Page : 648 pages
File Size : 41,6 Mb
Release : 2017-10-12
Category : Mathematics
ISBN : 9783319648675

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Matrix Algebra by James E. Gentle Pdf

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.

Author : Mohammad Sal Moslehian
Publisher : Springer Nature
Page : 763 pages
File Size : 42,7 Mb
Release : 2023-07-29
Category : Mathematics
ISBN : 9783031253867

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Matrix and Operator Equations and Applications by Mohammad Sal Moslehian Pdf

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.

Author : Randall E. Cline
Publisher : Unknown
Page : 104 pages
File Size : 51,9 Mb
Release : 1979
Category : Linear operators
ISBN : UOM:39015035721599

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Elements of the Theory of Generalized Inverses for Matrices by Randall E. Cline Pdf

Author : Stephen La Vern Campbell
Publisher : Pitman Advanced Publishing Program
Page : 292 pages
File Size : 40,8 Mb
Release : 1982
Category : Mathematics
ISBN : UCAL:B4509778

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Recent Applications of Generalized Inverses by Stephen La Vern Campbell Pdf

This collection of original papers shows the variety of current research into generalized inverses of linear transformations and their applications. The papers are grouped in sections, covering topics which include systems theory, operator theory, numerical methods, applications to Markov chains, and interpolation theory.