1.

Record Nr.

UNINA9910392729503321

Autore

Cvetković‐Ilić Dragana S

Titolo

Algebraic Properties of Generalized Inverses / / by Dragana S. Cvetković‐Ilić, Yimin Wei

Pubbl/distr/stampa

Singapore : , : Springer Singapore : , : Imprint : Springer, , 2017

ISBN

981-10-6349-4

Edizione

[1st ed. 2017.]

Descrizione fisica

1 online resource (VIII, 194 p.)

Collana

Developments in Mathematics, , 1389-2177 ; ; 52

Disciplina

371.805

Soggetti

Matrix theory

Algebra

Linear and Multilinear Algebras, Matrix Theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references at the end of each chapters and index.

Nota di contenuto

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.

Sommario/riassunto

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.