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Generalized Inverse Of Matrices And Its Applications
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Book Synopsis Generalized Inverse of Matrices and Its Applications by : Calyampudi Radhakrishna Rao
Download or read book Generalized Inverse of Matrices and Its Applications written by Calyampudi Radhakrishna Rao and published by John Wiley & Sons. This book was released on 1971 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Generalized Inverses by : Adi Ben-Israel
Download or read book Generalized Inverses written by Adi Ben-Israel and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Computation of Generalized Matrix Inverses and Applications by : Ivan Stanimirović
Download or read book Computation of Generalized Matrix Inverses and Applications written by Ivan Stanimirović and published by CRC Press. This book was released on 2017-12-14 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Generalized Inverses of Linear Transformations by : Stephen L. Campbell
Download or read book Generalized Inverses of Linear Transformations written by Stephen L. Campbell and published by SIAM. This book was released on 2009-03-26 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides comprehensive coverage of the mathematical theory of generalized inverses and a wide range of important and practical applications.
Book Synopsis Generalized Inverses and Applications by : M. Zuhair Nashed
Download or read book Generalized Inverses and Applications written by M. Zuhair Nashed and published by Elsevier. This book was released on 2014-05-10 with total page 1069 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Generalized Inverses: Theory and Computations by : Guorong Wang
Download or read book Generalized Inverses: Theory and Computations written by Guorong Wang and published by Springer. This book was released on 2018-05-12 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Generalized Inverses by : Ivan Kyrchei
Download or read book Generalized Inverses written by Ivan Kyrchei and published by Nova Science Publishers. This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"--
Book Synopsis Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition by : Haruo Yanai
Download or read book Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition written by Haruo Yanai and published by Springer Science & Business Media. This book was released on 2011-04-06 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Extremal Methods and Systems Analysis by : A. V. Fiacco
Download or read book Extremal Methods and Systems Analysis written by A. V. Fiacco and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers appearing in this Volume were selected from a collec tion of papers presented at the Internationa~ Symposium on Extrema~ Methods and Systems Ana~ysis on the Occasion of Professor A. Charnes' 60th Birthday, at the University of Texas in Austin, 13-15 September 1977. As coeditors, we have followed the normal editorial procedures of scholarly journals. We have obtained invaluable assistance from a number of colleagues who essentially performed the duties of associate editors, coordinating most of the reviews. All papers except those appearing in the Historica~ Perspectives section were refereed by at least two individuals with competency in the respective area. Because of the wide range and diversity of the topics, it would have been im possible for us to make a consistently rational selection of papers without the help of the associate editors and referees. We are indeed grateful to them. The breadth of extremal methods and systems analysis, suggested by the range of topics covered in these papers, is characteristic of the field and also of the scholarly work of Professor Charnes. Extre mal methods and systems analysis has been a pioneering and systematic approach to the development and application of new scientific theories and methods for problems of management and operations in both the pri vate and public sectors, spanning all major disciplines from economics to engineering.
Book Synopsis Optimization and Design of Geodetic Networks by : Erik W. Grafarend
Download or read book Optimization and Design of Geodetic Networks written by Erik W. Grafarend and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the period April 25th to May 10th, 1984 the 3rd Course of the International School of Advanced Geodesy entitled "Optimization and Design of Geodetic Networks" took place in Erice. The main subject of the course is clear from the title and consisted mainly of that particular branch of network analysis, which results from applying general concepts of mathematical optimization to the design of geodetic networks. As al ways when dealing with optimization problems, there is an a-priori choice of the risk (or gain) function which should be minimized (or maximized) according to the specific interest of the "designer", which might be either of a scientific or of an economic nature or even of both. These aspects have been reviewed in an intro ductory lecture in which the particular needs arising in a geodetic context and their analytical representations are examined. Subsequently the main body of the optimization problem, which has been conven tionally divided into zero, first, second and third order design problems, is presented. The zero order design deals with the estimability problem, in other words with the definition of which parameters are estimable from a given set of observa tions. The problem results from the fact that coordinates of points are not univocally determined from the observations of relative quantities such as angles and distances, whence a problem of the optimal choice of a reference system, the so-called "datum problem" arises.
Book Synopsis Matrix Algebra and Its Applications to Statistics and Econometrics by : Calyampudi Radhakrishna Rao
Download or read book Matrix Algebra and Its Applications to Statistics and Econometrics written by Calyampudi Radhakrishna Rao and published by World Scientific. This book was released on 1998 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: "I recommend this book for its extensive coverage of topics not easily found elsewhere and for its focus on applications".Zentralblatt MATH"The book is an excellent source on linear algebra, matrix theory and applications in statistics and econometrics, and is unique in many ways. I recommend it to anyone interested in these disciplines, and especially in how they benefit from one another".Statistical Papers, 2000
Book Synopsis Theory of Generalized Inverses Over Commutative Rings by : K.P.S. Bhaskara Rao
Download or read book Theory of Generalized Inverses Over Commutative Rings written by K.P.S. Bhaskara Rao and published by CRC Press. This book was released on 2002-03-21 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Elements of the Theory of Generalized Inverses of Matrices by : R.E. Cline
Download or read book Elements of the Theory of Generalized Inverses of Matrices written by R.E. Cline and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Applied Linear Algebra by : Stephen Boyd
Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Book Synopsis Generalized Inverses of Linear Transformations by : Stephen L. Campbell
Download or read book Generalized Inverses of Linear Transformations written by Stephen L. Campbell and published by SIAM. This book was released on 2009-01-01 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Matrix Partial Orders, Shorted Operators and Applications by : Sujit Kumar Mitra
Download or read book Matrix Partial Orders, Shorted Operators and Applications written by Sujit Kumar Mitra and published by World Scientific. This book was released on 2010 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Introduction. 1.1. Matrix orders. 1.2. Parallel sum and shorted operator. 1.3. A tour through the rest of the monograph -- 2. Matrix decompositions and generalized inverses. 2.1. Introduction. 2.2. Matrix decompositions. 2.3. Generalized inverse of a matrix. 2.4. The group inverse. 2.5. Moore-Penrose inverse. 2.6. Generalized inverses of modified matrices. 2.7. Simultaneous diagonalization. 2.8. Exercises -- 3. The minus order. 3.1. Introduction. 3.2. Space pre-order. 3.3. Minus order - some characterizations. 3.4. Matrices above/below a given matrix under the minus order. 3.5. Subclass of g-inverses A[symbol] of A such that [symbol]A = A[symbol]B and AA[symbol]=BA[symbol] when A
Book Synopsis Generalized Inverse Of Matrices Its Applications by : S.K. Mitra
Download or read book Generalized Inverse Of Matrices Its Applications written by S.K. Mitra and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
