Generalized Inverses

Adi Ben-Israel is Professor of Operations Research, Business and Mathematics at Rutgers University, New Brunswick, NJ. Previously he was Professor of Applied Mathematics at the University of Delaware, Northwestern University, and the Technion-Israel Institute of Technology. The late Thomas N.E. Greville was Professor of Mathematics, and a member of the US Army Mathematics Research Center at the University of Wisconsin, Madison, WI.

From the reviews of the second edition: "The book under review which is the second edition of the 30 years ago published one provides a detailed survey of generalized inverses and their main properties ... . An important feature of this book is the over 600 exercises ... . Each chapter ends with the section 'Suggested further reading'. These sections provide excellent additional references on topics treated ... . it can be used profitably by graduate or advanced undergraduate students of mathematics and computer science, and by PhD students ... ." (Robert Rajko, Acta Scientiarum Mathematicarum, Vol. 71, 2005) "Each chapter is accompanied by suggestions for further reading, while the bibliography contains 901 references. ... The book contains 450 exercises at different levels of difficulty, many of which are solved in detail. This feature makes it suitable either for reference and self-study or for use as a classroom text. It can be used profitably by graduate students or advanced undergraduate students ... ." (Nicholas Karampetakis, Zentralblatt MATH, Vol. 1026, 2004)

• Preliminaries.- Existence and Construction of Generalized Inverses.- Linear Systems and Characterization of Generalized Inverses.- Minimal Properties of Generalized Inverses.- Spectral Generalized Inverses.- Generalized Inverses of Partitioned Matrices.- A Spectral Theory for Rectangular Matrices.- Computational Aspects of Generalized Inverses.- Miscellaneous Applications.- Generalized Inverses of Linear Operators between Hilbert Spaces.