Overview
- Describes the developments in the research directions and the types of the generalized inverses since mid-1970s
- Includes the fundamentals as well as advanced topics
- Ready to be adopted as a textbook or reference book for graduate courses
Part of the book series: Developments in Mathematics (DEVM, volume 53)
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About this book
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.
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Keywords
Table of contents (12 chapters)
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Front Matter
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Back Matter
Reviews
“The book presents a theoretical study of the generalization of Cramer's rule and determinant representations, reverse order laws of matrix products, parallel computations, perturbation analysis, weighted Moore-Penrose inverses, factorization methods, singular value decompositions, embedding methods, finite methods for generalized inverses. Each chapter ends with remarks and a list of related references. The book can be useful for graduate students having a good background in linear algebra and researchers interested in inversion problems.” (Mohammad Sal Moslehian, zbMATH 1395.15002, 2018)
Authors and Affiliations
Bibliographic Information
Book Title: Generalized Inverses: Theory and Computations
Authors: Guorong Wang, Yimin Wei, Sanzheng Qiao
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-981-13-0146-9
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. and Science Press 2018
Hardcover ISBN: 978-981-13-0145-2Published: 24 May 2018
Softcover ISBN: 978-981-13-4340-7Published: 11 February 2019
eBook ISBN: 978-981-13-0146-9Published: 12 May 2018
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: XIX, 378
Number of Illustrations: 6 b/w illustrations
Additional Information: Jointly published with Science Press, Beijing, China
Topics: Linear and Multilinear Algebras, Matrix Theory, Operator Theory, Computational Mathematics and Numerical Analysis