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

Format:

Book

Author/Creator:

Cvetković‐Ilić, Dragana S., Author.

Wei, Yimin., Author.

Series:

Developments in Mathematics, 2197-795X ; 52

Language:

English

Subjects (All):

Algebras, Linear.

Linear Algebra.

Local Subjects:

Linear Algebra.

Physical Description:

1 online resource (VIII, 194 p.)

Edition:

1st ed. 2017.

Place of Publication:

Singapore : Springer Nature Singapore : Imprint: Springer, 2017.

Summary:

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.

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.

Notes:

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

ISBN:

981-10-6349-4