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Generalized Inverses And Applications

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Generalized Inverses

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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.

Generalized Inverses

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Author : Adi Ben-Israel
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-16

Theory Of Generalized Inverses Over Commutative Rings

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Author : K.P.S. Bhaskara Rao
language : en
Publisher: CRC Press
Release Date : 2002-03-21

Theory Of Generalized Inverses Over Commutative Rings written by K.P.S. Bhaskara Rao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-03-21 with Mathematics categories.

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. The subject of generalized inverses of matrices over rings has now reached a state suitable for a comprehensive treatment - this book provides just that, for mathematicians, algebraists and control theorists.

Generalized Inverses Of Linear Transformations

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Author : Stephen L. Campbell
language : en
Publisher: SIAM
Release Date : 2009-03-26

Generalized Inverses Of Linear Transformations written by Stephen L. Campbell and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-26 with Mathematics categories.

Provides comprehensive coverage of the mathematical theory of generalized inverses and a wide range of important and practical applications.

Generalized Inverses Theory And Computations

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Author : Guorong Wang
language : en
Publisher: Springer
Release Date : 2018-05-12

Generalized Inverses Theory And Computations written by Guorong Wang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-12 with Mathematics categories.

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.

Generalized Inverses And Applications

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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.

Projection Matrices Generalized Inverse Matrices And Singular Value Decomposition

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Author : Haruo Yanai
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-06

Projection Matrices Generalized Inverse Matrices And Singular Value Decomposition written by Haruo Yanai 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 2011-04-06 with Mathematics categories.

Aside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because it is closely related to the former. The book provides systematic and in-depth accounts of these concepts from a unified viewpoint of linear transformations finite dimensional vector spaces. More specially, it shows that projection matrices (projectors) and g-inverse matrices can be defined in various ways so that a vector space is decomposed into a direct-sum of (disjoint) subspaces. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition will be useful for researchers, practitioners, and students in applied mathematics, statistics, engineering, behaviormetrics, and other fields.

Matrix Theory

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Author : Robert Piziak
language : en
Publisher: CRC Press
Release Date : 2007-02-22

Matrix Theory written by Robert Piziak and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-22 with Mathematics categories.

In 1990, the National Science Foundation recommended that every college mathematics curriculum should include a second course in linear algebra. In answer to this recommendation, Matrix Theory: From Generalized Inverses to Jordan Form provides the material for a second semester of linear algebra that probes introductory linear algebra concepts while also exploring topics not typically covered in a sophomore-level class. Tailoring the material to advanced undergraduate and beginning graduate students, the authors offer instructors flexibility in choosing topics from the book. The text first focuses on the central problem of linear algebra: solving systems of linear equations. It then discusses LU factorization, derives Sylvester's rank formula, introduces full-rank factorization, and describes generalized inverses. After discussions on norms, QR factorization, and orthogonality, the authors prove the important spectral theorem. They also highlight the primary decomposition theorem, Schur's triangularization theorem, singular value decomposition, and the Jordan canonical form theorem. The book concludes with a chapter on multilinear algebra. With this classroom-tested text students can delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.

Generalized Inverses

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Author : Ivan Kyrchei
language : en
Publisher: Nova Science Publishers
Release Date : 2022

Generalized Inverses written by Ivan Kyrchei and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Mathematics categories.

"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"--

Linear Model Theory

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Author : Dale L. Zimmerman
language : en
Publisher: Springer Nature
Release Date : 2020-11-02

Linear Model Theory written by Dale L. Zimmerman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-02 with Mathematics categories.

This textbook presents a unified and rigorous approach to best linear unbiased estimation and prediction of parameters and random quantities in linear models, as well as other theory upon which much of the statistical methodology associated with linear models is based. The single most unique feature of the book is that each major concept or result is illustrated with one or more concrete examples or special cases. Commonly used methodologies based on the theory are presented in methodological interludes scattered throughout the book, along with a wealth of exercises that will benefit students and instructors alike. Generalized inverses are used throughout, so that the model matrix and various other matrices are not required to have full rank. Considerably more emphasis is given to estimability, partitioned analyses of variance, constrained least squares, effects of model misspecification, and most especially prediction than in many other textbooks on linear models. This book is intended for master and PhD students with a basic grasp of statistical theory, matrix algebra and applied regression analysis, and for instructors of linear models courses. Solutions to the book’s exercises are available in the companion volume Linear Model Theory - Exercises and Solutions by the same author.

Generalized Inverses And Applications

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