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Developments in Mathematics

Generalized Inverses: Theory and Computations

Authors: Wang, Guorong, Wei, Yimin, Qiao, Sanzheng

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  • Describes the developments in the research directions and the types of the generalized inverses since mid-1970s
    Includes the fundamentals as well as advanced topics
    Ready to be adopted as a textbook or reference book for graduate courses

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eBook $99.00
price for USA in USD (gross)
  • ISBN 978-981-13-0146-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA in USD
  • ISBN 978-981-13-0145-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA in USD
  • ISBN 978-981-13-4340-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics.

It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.


Reviews

“The book presents a theoretical study of the generalization of Cramer's rule and determinant representations, reverse order laws of matrix products, parallel computations, perturbation analysis, weighted Moore-Penrose inverses, factorization methods, singular value decompositions, embedding methods, finite methods for generalized inverses. Each chapter ends with remarks and a list of related references. The book can be useful for graduate students having a good background in linear algebra and researchers interested in inversion problems.” (Mohammad Sal Moslehian, zbMATH 1395.15002, 2018)

Table of contents (12 chapters)

Table of contents (12 chapters)
  • Equation Solving Generalized Inverses

    Pages 1-64

    Wang, Guorong (et al.)

  • Drazin Inverse

    Pages 65-90

    Wang, Guorong (et al.)

  • Generalization of the Cramer’s Rule and the Minors of the Generalized Inverses

    Pages 91-151

    Wang, Guorong (et al.)

  • Reverse Order and Forward Order Laws for $$A_{T,S}^{(2)}$$

    Pages 153-174

    Wang, Guorong (et al.)

  • Computational Aspects

    Pages 175-224

    Wang, Guorong (et al.)

Buy this book

eBook $99.00
price for USA in USD (gross)
  • ISBN 978-981-13-0146-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA in USD
  • ISBN 978-981-13-0145-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA in USD
  • ISBN 978-981-13-4340-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Generalized Inverses: Theory and Computations
Authors
Series Title
Developments in Mathematics
Series Volume
53
Copyright
2018
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd. and Science Press
eBook ISBN
978-981-13-0146-9
DOI
10.1007/978-981-13-0146-9
Hardcover ISBN
978-981-13-0145-2
Softcover ISBN
978-981-13-4340-7
Series ISSN
1389-2177
Edition Number
1
Number of Pages
XIX, 378
Number of Illustrations
6 b/w illustrations
Additional Information
Jointly published with Science Press, Beijing, China
Topics