Generalized Inverse Matrices
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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.
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 Of Linear Transformations
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Author : Stephen L. Campbell
language : en
Publisher: SIAM
Release Date : 2009-01-01
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 2009-01-01 with Mathematics categories.
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.
Generalized Inverse Of Matrices And Its Applications
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Author : Calyampudi Radhakrishna Rao
language : en
Publisher: John Wiley & Sons
Release Date : 1971
Generalized Inverse Of Matrices And Its Applications written by Calyampudi Radhakrishna Rao 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 1971 with Mathematics categories.
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.
Elements Of The Theory Of Generalized Inverses Of Matrices
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Author : R.E. Cline
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Elements Of The Theory Of Generalized Inverses Of Matrices written by R.E. Cline 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 2012-12-06 with Mathematics categories.
The purpose of this monograph is to provide a concise introduction to the theory of generalized inverses of matrices that is accessible to undergraduate mathematics majors. Although results from this active area of research have appeared in a number of excellent graduate level text books since 1971, material for use at the undergraduate level remains fragmented. The basic ideas are so fundamental, however, that they can be used to unify various topics that an undergraduate has seen but perhaps not related. Material in this monograph was first assembled by the author as lecture notes for the senior seminar in mathematics at the University of Tennessee. In this seminar one meeting per week was for a lecture on the subject matter, and another meeting was to permit students to present solutions to exercises. Two major problems were encountered the first quarter the seminar was given. These were that some of the students had had only the required one-quarter course in matrix theory and were not sufficiently familiar with eigenvalues, eigenvectors and related concepts, and that many -v- of the exercises required fortitude. At the suggestion of the UMAP Editor, the approach in the present monograph is (1) to develop the material in terms of full rank factoriza tions and to relegate all discussions using eigenvalues and eigenvectors to exercises, and (2) to include an appendix of hints for exercises.
Generalized Inverses Algorithms And Applications
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Author : Ivan Kyrchei
language : en
Publisher:
Release Date : 2021-12-31
Generalized Inverses Algorithms And Applications written by Ivan Kyrchei and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-31 with 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.
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 Inverse Matrices
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Author : T. L. Boullion
language : en
Publisher: Wiley-Interscience
Release Date : 1971-07-02
Generalized Inverse Matrices written by T. L. Boullion and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-07-02 with Mathematics categories.
Definitions and fundamental properties; Pseudoinverses of sums and products; Generalized inverses with spectral properties; Special topics; Special topics; Solving systems of linear equations; Applications; Appendices; Index.
Combinatorial Matrix Theory And Generalized Inverses Of Matrices
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Author : Ravindra B. Bapat
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-11
Combinatorial Matrix Theory And Generalized Inverses Of Matrices written by Ravindra B. Bapat 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 2013-02-11 with Mathematics categories.
This book consists of eighteen articles in the area of `Combinatorial Matrix Theory' and `Generalized Inverses of Matrices'. Original research and expository articles presented in this publication are written by leading Mathematicians and Statisticians working in these areas. The articles contained herein are on the following general topics: `matrices in graph theory', `generalized inverses of matrices', `matrix methods in statistics' and `magic squares'. In the area of matrices and graphs, speci_c topics addressed in this volume include energy of graphs, q-analog, immanants of matrices and graph realization of product of adjacency matrices. Topics in the book from `Matrix Methods in Statistics' are, for example, the analysis of BLUE via eigenvalues of covariance matrix, copulas, error orthogonal model, and orthogonal projectors in the linear regression models. Moore-Penrose inverse of perturbed operators, reverse order law in the case of inde_nite inner product space, approximation numbers, condition numbers, idempotent matrices, semiring of nonnegative matrices, regular matrices over incline and partial order of matrices are the topics addressed under the area of theory of generalized inverses. In addition to the above traditional topics and a report on CMTGIM 2012 as an appendix, we have an article on old magic squares from India.
Computation Of Generalized Matrix Inverses And Applications
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Author : Ivan Stanimirović
language : en
Publisher: CRC Press
Release Date : 2017-12-14
Computation Of Generalized Matrix Inverses And Applications written by Ivan Stanimirović and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-14 with Mathematics categories.
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.