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Author: Stephen L. Campbell
Publisher: SIAM
Published: 2009-03-26
Total Pages: 288
ISBN-13: 0898716713
DOWNLOAD EBOOK →Provides comprehensive coverage of the mathematical theory of generalized inverses and a wide range of important and practical applications.
Author: Dragana S. Cvetković‐Ilić
Publisher: Springer
Published: 2017-10-07
Total Pages: 203
ISBN-13: 9811063494
DOWNLOAD EBOOK →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:
Published: 2017
Total Pages:
ISBN-13: 9789811063503
DOWNLOAD EBOOK →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: Jianlong Chen
Publisher: Springer Nature
Published:
Total Pages: 331
ISBN-13: 9819982855
DOWNLOAD EBOOK →Author: Guorong Wang
Publisher: Springer
Published: 2018-05-12
Total Pages: 378
ISBN-13: 9811301468
DOWNLOAD EBOOK →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: Mohammad Maruf Ahmed
Publisher: LAP Lambert Academic Publishing
Published: 2011-02
Total Pages: 80
ISBN-13: 9783843393485
DOWNLOAD EBOOK →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: Yimin Wei
Publisher: World Scientific
Published: 2018-07-18
Total Pages: 472
ISBN-13: 9813238682
DOWNLOAD EBOOK →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: University of Wisconsin--Madison. Mathematics Research Center
Publisher:
Published: 1976
Total Pages: 1082
ISBN-13:
DOWNLOAD EBOOK →Author: K.P.S. Bhaskara Rao
Publisher: CRC Press
Published: 2002-03-21
Total Pages: 192
ISBN-13: 9780415272483
DOWNLOAD EBOOK →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 elements in a ring, regular matrices over principal ideal rings, and regular matrices over commutative rings. Students, mathematicians working in g-inverses of matrices, along with algebraists, and control theorists will find new and indispensable data, presented with clarity and insight. This book is also well suited to graduate courses on g-inverses in algebra.
