Algebraic Properties of Generalized Inverses

Dragana S. Cvetković‐Ilić, Yimin Wei (Autoren)

Buch | Softcover

194 Seiten

2018 | Softcover reprint of the original 1st ed. 2017
Springer Verlag, Singapore
978-981-13-4862-4 (ISBN)

Artikel merken

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.

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).

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.

Erscheinungsdatum	04.03.2022
Reihe/Serie	Developments in Mathematics ; 52
Zusatzinfo	VIII, 194 p.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Schlagworte	Drazin inverse • generalized and hypergeneralized • Idempotent • Moore-Penrose inverse • Operators on Banach spaces • Reverse order law
ISBN-10	981-13-4862-6 / 9811348626
ISBN-13	978-981-13-4862-4 / 9789811348624
Zustand	Neuware