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| Author | : Dragana S. Cvetković‐Ilić |
| Publisher | : Springer |
| Total Pages | : 203 |
| Release | : 2017-10-07 |
| Genre | : Mathematics |
| ISBN | : 9811063494 |
Download Algebraic Properties of Generalized Inverses Book in PDF, ePub and Kindle
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.
| Author | : Dragana S. Cvetković Ilić |
| Publisher | : |
| Total Pages | : |
| Release | : 2017 |
| Genre | : Linear operators |
| ISBN | : 9789811063503 |
Download Algebraic Properties of Generalized Inverses Book in PDF, ePub and Kindle
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.--
| Author | : Adi Ben-Israel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 433 |
| Release | : 2006-04-18 |
| Genre | : Mathematics |
| ISBN | : 0387216340 |
Download Generalized Inverses Book in PDF, ePub and Kindle
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.
| Author | : Jianlong Chen |
| Publisher | : Springer Nature |
| Total Pages | : 331 |
| Release | : |
| Genre | : |
| ISBN | : 9819982855 |
Download Algebraic Theory of Generalized Inverses Book in PDF, ePub and Kindle
| Author | : Stephen L. Campbell |
| Publisher | : SIAM |
| Total Pages | : 289 |
| Release | : 2009-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898719046 |
Download Generalized Inverses of Linear Transformations Book in PDF, ePub and Kindle
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.
| Author | : Guorong Wang |
| Publisher | : Springer |
| Total Pages | : 390 |
| Release | : 2018-05-12 |
| Genre | : Mathematics |
| ISBN | : 9811301468 |
Download Generalized Inverses: Theory and Computations Book in PDF, ePub and Kindle
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.
| Author | : M. Zuhair Nashed |
| Publisher | : Elsevier |
| Total Pages | : 1069 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483270297 |
Download Generalized Inverses and Applications Book in PDF, ePub and Kindle
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.
| Author | : Yimin Wei |
| Publisher | : World Scientific |
| Total Pages | : 472 |
| Release | : 2018-07-18 |
| Genre | : Mathematics |
| ISBN | : 9813238682 |
Download Numerical And Symbolic Computations Of Generalized Inverses Book in PDF, ePub and Kindle
We introduce new methods connecting numerics and symbolic computations, i.e., both the direct and iterative methods as well as the symbolic method for computing the generalized inverses. These will be useful for Engineers and Statisticians, in addition to applied mathematicians.Also, main applications of generalized inverses will be presented. Symbolic method covered in our book but not discussed in other book, which is important for numerical-symbolic computations.
| Author | : Mohammad Maruf Ahmed |
| Publisher | : LAP Lambert Academic Publishing |
| Total Pages | : 80 |
| Release | : 2011-02 |
| Genre | : |
| ISBN | : 9783843393485 |
Download Generalized Inverse Book in PDF, ePub and Kindle
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.
| Author | : K.P.S. Bhaskara Rao |
| Publisher | : CRC Press |
| Total Pages | : 192 |
| Release | : 2002-03-21 |
| Genre | : Mathematics |
| ISBN | : 0203218876 |
Download Theory of Generalized Inverses Over Commutative Rings Book in PDF, ePub and Kindle
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
