Algebraic Properties of Generalized Inverses

by Dragana S. Cvetkovic-Ilic, Yimin Wei

Overview

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.

Product Details

ISBN-13:	9789811063480
Publisher:	Springer Nature Singapore
Publication date:	10/08/2017
Series:	Developments in Mathematics , #52
Edition description:	1st ed. 2017
Pages:	194
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

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).

Table of Contents

Definitions and motivations.- Reverse order law.- Completions of operator matrices and generalized inverses.- Generalized inverses and idempotents.- Drazin inverse of a 2 × 2 block matrix.- Additive Results for the Drazin Inverse.- Index.

Editorial 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)

From the Publisher