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Generalized Inverses and Applications

Author: M. Zuhair Nashed

Publisher: Elsevier

Published: 2014-05-10

Total Pages: 1069

ISBN-13: 1483270297

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.

Generalized Inverses

Author: Adi Ben-Israel

Publisher: Springer Science & Business Media

Published: 2006-04-18

Total Pages: 433

ISBN-13: 0387216340

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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 of Linear Transformations

Author: Stephen L. Campbell

Publisher: SIAM

Published: 2009-03-26

Total Pages: 288

ISBN-13: 0898716713

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

Theory of Generalized Inverses Over Commutative Rings

Author: K.P.S. Bhaskara Rao

Publisher: CRC Press

Published: 2002-03-21

Total Pages: 192

ISBN-13: 0203218876

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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

Computation of Generalized Matrix Inverses and Applications

Author: Ivan Stanimirović

Publisher: CRC Press

Published: 2017-12-14

Total Pages: 199

ISBN-13: 1351630059

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This volume offers a gradual exposition to matrix theory as a subject of linear algebra. It presents both the theoretical results in generalized matrix inverses and the applications. The book is as self-contained as possible, assuming no prior knowledge of matrix theory and linear algebra. The book first addresses the basic definitions and concepts of an arbitrary generalized matrix inverse with special reference to the calculation of {i,j,...,k} inverse and the Moore–Penrose inverse. Then, the results of LDL* decomposition of the full rank polynomial matrix are introduced, along with numerical examples. Methods for calculating the Moore–Penrose’s inverse of rational matrix are presented, which are based on LDL* and QDR decompositions of the matrix. A method for calculating the A(2)T;S inverse using LDL* decomposition using methods is derived as well as the symbolic calculation of A(2)T;S inverses using QDR factorization. The text then offers several ways on how the introduced theoretical concepts can be applied in restoring blurred images and linear regression methods, along with the well-known application in linear systems. The book also explains how the computation of generalized inverses of matrices with constant values is performed. It covers several methods, such as methods based on full-rank factorization, Leverrier–Faddeev method, method of Zhukovski, and variations of the partitioning method.

Generalized Inverses: Theory and Computations

Author: Guorong Wang

Publisher: Springer

Published: 2018-05-12

Total Pages: 378

ISBN-13: 9811301468

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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: Algorithms and Applications

Author: Ivan Kyrchei

Publisher:

Published: 2021-12-31

Total Pages:

ISBN-13: 9781685073565

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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.

Generalized Inverse of Matrices and Its Applications

Author: Calyampudi Radhakrishna Rao

Publisher: John Wiley & Sons

Published: 1971

Total Pages: 264

ISBN-13:

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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.

Generalized Inverses of Linear Transformations

Author: Stephen L. Campbell

Publisher: SIAM

Published: 2009-01-01

Total Pages: 289

ISBN-13: 0898719046

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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.

Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition

Author: Haruo Yanai

Publisher: Springer Science & Business Media

Published: 2011-04-06

Total Pages: 244

ISBN-13: 144199887X

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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.