Elements of the Theory of Generalized Inverses of Matrices

Elements of the Theory of Generalized Inverses of Matrices by R.E. Cline.

The purpose of this monograph is to provide a concise introduction to the theory of generalized inverses of matrices that is accessible to undergraduate mathematics majors. Although results from this active area of research have appeared in a number of excellent graduate level text­ books since 1971...

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Bibliographic Details
Main Author: Cline, R.E (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 1979.
Edition:1st ed. 1979.
Series:Modules and Monographs in Undergraduate Mathematics and Its Applications
Springer eBook Collection.
Subjects:
Matrix theory.
Algebra.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1. Introduction
  • 1.1 Preliminary Remarks
  • 1.2 Matrix Notation and Terminology
  • 1.3 A Rationale for Generalized Inverses
  • 2. Systems of Equations and the Moore-Penrose Inverse of a Matrix
  • 2.1 Zero, One or Many Solutions of Ax = b
  • 2.2 Full Rank Factorizations and the Moore-Penrose Inverse
  • 2.3 Some Geometric Illustrations
  • 2.4 Miscellaneous Exercises
  • 3. More on Moore-Penrose Inverses
  • 3.1 Basic Properties of A+
  • 3.2 Applications with Matrices of Special Structure
  • 3.3 Miscellaneous Exercises
  • 4. Drazin Inverses
  • 4.1 The Drazin Inverse of a Square Matrix
  • 4.2 An Extension to Rectangular Matrices
  • 4.3 Expressions Relating Ad and A+
  • 4.4 Miscellaneous Exercises
  • 5. Other Generalized Inverses
  • 5.1 Inverses That Are Not Unique
  • Appendix 1: Hints for Certain Exercises
  • Appendix 2: Selected References
  • Index to Principal Definitions.

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