Download or read book Algebraic Properties of Generalized Inverses written by Dragana S. Cvetković‐Ilić and published by Springer. This book was released on 2017-10-07 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic Properties of Generalized Inverses written by Dragana S. Cvetković Ilić and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.--
Download or read book Algebraic Theory of Generalized Inverses written by Jianlong Chen and published by Springer Nature. This book was released on with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
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.
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.
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.
Download or read book Generalized Inverse written by Mohammad Maruf Ahmed and published by LAP Lambert Academic Publishing. This book was released on 2011-02 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: A growing interest in the theory of generalized inverses and in applications of generalized inverses in such fields as engineering and statistics has stimulated an interest in teaching about generalized inverses in linear algebra courses. When A is a nonsingular matrix, the equation Ax=b has a unique solution.The generalized inverse of a singular matrix can be motivated as generalization of this situation. In fact, the solution will be the unique solution to Ax=b when a unique solution exists, will be a solution when there is more than one solution, and will be a least squares solution when no solution exists. Generalized inverse can also be applied to network theory and in optimizing problems. Beside this, generalized inverse can be represented by contour integrations. We can directly calculate generalized inverse by the special Mathematica command PseudoInverse.
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
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"--
Download or read book Recent Applications of Generalized Inverses written by Stephen La Vern Campbell and published by Pitman Advanced Publishing Program. This book was released on 1982 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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
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.
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.
Download or read book TEXTBOOK OF MATRIX ALGEBRA written by SUDDHENDU BISWAS and published by PHI Learning Pvt. Ltd.. This book was released on 2012-08-07 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended as a text for postgraduate and undergraduate honours students of Statistics, Mathematics, Operations Research as well as students in various branches of Engineering, this student-friendly book gives an indepth analysis of Matrix Algebra and all the major topics related to it. Divided into 12 chapters, the book begins with a discussion on Elements of Matrix Theory and Some Special Matrices. Then it goes on to give a detailed discussion on Scalar Function and Inverse of a Matrix, Rank of a Matrix, Generalized Inverse of a Matrix, and Quadric Forms and Inequalities. The book concludes by giving Some Applications of Algebra of Matrices, Matrices in the Infinite Dimensional Vector Space, and Computational Tracts in Matrices. KEY FEATURES Gives a large number of both solved and unsolved problems of Elementary Matrix. Provides an exhaustive treatment of Generalized Inverse Matrix with many applications in Statistics. Devotes one chapter exclusively to application of Matrices. Provides one full chapter on Matrices in the Infinite Dimensional Vector Space, which will be quite useful for postgraduate students. Gives an Appendix on R Software which will be extremely useful for students of Statistics. Provides Question Bank which will greatly benefit both undergraduate and postgraduate students. This book, which beautifully blends both theory and applications of Matrix Algebra, should prove to be an invaluable text for the students.
Download or read book Generalized Inverses and Operator Theory written by Selwyn Ross Caradus and published by Kingston, Ont. : Queen's University. This book was released on 1978 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
