TY  - BOOK
AU  - Cvetković‐Ilić,Dragana S.
AU  - Wei,Yimin
ED  - SpringerLink (Online service)
TI  - Algebraic Properties of Generalized Inverses
T2  - Developments in Mathematics,
SN  - 9789811063497
AV  - QA184-205 
U1  - 512.5 23
PY  - 2017///
CY  - Singapore
PB  - Springer Singapore, Imprint: Springer
KW  - Matrix theory
KW  - Linear and Multilinear Algebras, Matrix Theory
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-981-10-6349-7
ER  -