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Generalized Inverses: Theory and Computations

  • Book
  • © 2018

Overview

Authors:
  1. Guorong Wang

    1. Department of Mathematics, Shanghai Normal University, Shanghai, China

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  2. Yimin Wei

    1. Department of Mathematics, Fudan University, Shanghai, China

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    You can also search for this author in PubMed   Google Scholar

  3. Sanzheng Qiao

    1. Department of Computing and Software, McMaster University, Hamilton, Canada

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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

Part of the book series: Developments in Mathematics (DEVM, volume 53)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xix
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  2. Equation Solving Generalized Inverses

    • Guorong Wang, Yimin Wei, Sanzheng Qiao
    Pages 1-64

  3. Drazin Inverse

    • Guorong Wang, Yimin Wei, Sanzheng Qiao
    Pages 65-90

  4. Generalization of the Cramer’s Rule and the Minors of the Generalized Inverses

    • Guorong Wang, Yimin Wei, Sanzheng Qiao
    Pages 91-151

  5. Reverse Order and Forward Order Laws for \(A_{T,S}^{(2)}\)

    • Guorong Wang, Yimin Wei, Sanzheng Qiao
    Pages 153-174

  6. Computational Aspects

    • Guorong Wang, Yimin Wei, Sanzheng Qiao
    Pages 175-224

  7. Structured Matrices and Their Generalized Inverses

    • Guorong Wang, Yimin Wei, Sanzheng Qiao
    Pages 225-231

  8. Parallel Algorithms for Computing the Generalized Inverses

    • Guorong Wang, Yimin Wei, Sanzheng Qiao
    Pages 233-261

  9. Perturbation Analysis of the Moore-Penrose Inverse and the Weighted Moore-Penrose Inverse

    • Guorong Wang, Yimin Wei, Sanzheng Qiao
    Pages 263-289

  10. Perturbation Analysis of the Drazin Inverse and the Group Inverse

    • Guorong Wang, Yimin Wei, Sanzheng Qiao
    Pages 291-306

  11. Generalized Inverses of Polynomial Matrices

    • Guorong Wang, Yimin Wei, Sanzheng Qiao
    Pages 307-316

  12. Moore-Penrose Inverse of Linear Operators

    • Guorong Wang, Yimin Wei, Sanzheng Qiao
    Pages 317-338

  13. Operator Drazin Inverse

    • Guorong Wang, Yimin Wei, Sanzheng Qiao
    Pages 339-373

  14. Back Matter

    Pages 375-378
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Keywords

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)

Authors and Affiliations

  • Department of Mathematics, Shanghai Normal University, Shanghai, China

    Guorong Wang

  • Department of Mathematics, Fudan University, Shanghai, China

    Yimin Wei

  • Department of Computing and Software, McMaster University, Hamilton, Canada

    Sanzheng Qiao

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