Developments in Mathematics

Algebraic Properties of Generalized Inverses

Authors: Cvetković‐Ilić, Dragana S., Wei, Yimin

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  • Discuss the open problems relevant to each particular topic
  • Investigates the algebraic properties of the Drazin inverse
  • Covers the latest references on the generalized inverses
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eBook 41,64 €
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  • ISBN 978-981-10-6349-7
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Hardcover 49,99 €
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  • ISBN 978-981-10-6348-0
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Softcover 49,99 €
price for China (P.R.) (gross)
  • ISBN 978-981-13-4862-4
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  • Usually dispatched within 3 to 5 business days.
About this book

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.

About the authors

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).

Reviews

“The presentation is very clear. The proofs are described in detail. Another beautiful feature of this book is that each chapter ends with references. … Graduate students, Ph.D. students and researchers working on the theory of generalized inverses or closely related fields will benefit from this book.” (Debasisha Mishra, Mathematical Reviews, May, 2018)

“This book gives a presentation of some current topics in theory of generalized inverses. … This book is well written and quite useful for the matrix theory. This reviewer will recommend it as the textbook for the under-graduate, graduate students and PhD students but also for all the researchers interested in this topic.” (Nestor Thome, zbMATH 1380.15003, 2018)

Table of contents (6 chapters)

  • Definitions and Motivations

    Cvetković Ilić, Dragana S. (et al.)

    Pages 1-10

    Preview Buy Chapter 24,95 €
  • Reverse Order Law

    Cvetković Ilić, Dragana S. (et al.)

    Pages 11-50

    Preview Buy Chapter 24,95 €
  • Completions of Operator Matrices and Generalized Inverses

    Cvetković Ilić, Dragana S. (et al.)

    Pages 51-88

    Preview Buy Chapter 24,95 €
  • Generalized Inverses and Idempotents

    Cvetković Ilić, Dragana S. (et al.)

    Pages 89-108

    Preview Buy Chapter 24,95 €
  • Drazin Inverse of a $$2 \times 2$$ Block Matrix

    Cvetković Ilić, Dragana S. (et al.)

    Pages 109-158

    Preview Buy Chapter 24,95 €

Buy this book

eBook 41,64 €
price for China (P.R.) (gross)
  • ISBN 978-981-10-6349-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 49,99 €
price for China (P.R.) (gross)
  • ISBN 978-981-10-6348-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover 49,99 €
price for China (P.R.) (gross)
  • ISBN 978-981-13-4862-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Properties of Generalized Inverses
Authors
Series Title
Developments in Mathematics
Series Volume
52
Copyright
2017
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-10-6349-7
DOI
10.1007/978-981-10-6349-7
Hardcover ISBN
978-981-10-6348-0
Softcover ISBN
978-981-13-4862-4
Series ISSN
1389-2177
Edition Number
1
Number of Pages
VIII, 194
Topics