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© 2017

Algebraic Properties of Generalized Inverses

Book

Part of the Developments in Mathematics book series (DEVM, volume 52)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Dragana S. Cvetković Ilić, Yimin Wei
    Pages 1-10
  3. Dragana S. Cvetković Ilić, Yimin Wei
    Pages 11-50
  4. Dragana S. Cvetković Ilić, Yimin Wei
    Pages 51-88
  5. Dragana S. Cvetković Ilić, Yimin Wei
    Pages 89-108
  6. Dragana S. Cvetković Ilić, Yimin Wei
    Pages 109-158
  7. Dragana S. Cvetković Ilić, Yimin Wei
    Pages 159-192
  8. Back Matter
    Pages 193-194

About this book

Introduction

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.

Keywords

Drazin inverse idempotent generalized and hypergeneralized Reverse order law Operators on Banach spaces Moore-Penrose inverse

Authors and affiliations

  1. 1.Faculty of Science and MathematicsUniversity of NisNisSerbia
  2. 2.School of Mathematical SciencesFudan UniversityShanghaiChina

About the authors

Dragana S. Cvetković‐Ilić is a Professor of Mathematics at the Faculty of Science and Mathematics, University of Nis. She has written in collaboration with other coauthors many articles with a significant contribution to the theory of generalized inverses, linear algebra and operator theory.

Yimin Wei is a Professor at the School of Mathematical Sciences, Fudan University, Shanghai, P.R. of China. He has published four English monographs and over 100 research papers in international journals.

His researches focus on linear algebra, matrix computations in control, and multi-linear algebra (tensors).

Bibliographic information

  • Book Title Algebraic Properties of Generalized Inverses
  • Authors Dragana S. Cvetković‐Ilić
    Yimin Wei
  • Series Title Developments in Mathematics
  • Series Abbreviated Title DEVM
  • DOI https://doi.org/10.1007/978-981-10-6349-7
  • Copyright Information Springer Nature Singapore Pte Ltd. 2017
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-981-10-6348-0
  • Softcover ISBN 978-981-13-4862-4
  • eBook ISBN 978-981-10-6349-7
  • Series ISSN 1389-2177
  • Series E-ISSN 2197-795X
  • Edition Number 1
  • Number of Pages VIII, 194
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Linear and Multilinear Algebras, Matrix Theory
  • Buy this book on publisher's site
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Reviews

“The presentation is very clear. The proofs are described in detail. Another beautiful feature of this book is that each chapter ends with references. … Graduate students, Ph.D. students and researchers working on the theory of generalized inverses or closely related fields will benefit from this book.” (Debasisha Mishra, Mathematical Reviews, May, 2018)

“This book gives a presentation of some current topics in theory of generalized inverses. … This book is well written and quite useful for the matrix theory. This reviewer will recommend it as the textbook for the under-graduate, graduate students and PhD students but also for all the researchers interested in this topic.” (Nestor Thome, zbMATH 1380.15003, 2018)