Algebraic Properties of Generalized Inverses

1. Auflage 2017
ISBN: 978-981-10-6348-0
Verlag: Springer Nature Singapore

Buch, Englisch, Band 52, 194 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 4321 g

Reihe: Developments in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Wei, Yimin

Cvetkovic-Ilic, Dragana S.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Inhaltsverzeichnis

De?nitions 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.

Über Autor(innen)

Dragana S. Cvetkovic-Ilic 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).