This second edition accounts for many major developments in generalized inverses while maintaining the informal and leisurely style of the 1974 first edition. Added material includes a chapter on applications, new exercises, and an appendix on the work of E.H. Moore.
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Editorial Reviews
Review
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 … ." (Róbert Rajkó, 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)
From the Back Cover
The field of generalized inverses has grown much since the appearance of the first edition in 1974, and is still growing. This book accounts for these developments while maintaining the informal and leisurely style of the first edition. New material has been added, including many theoretical results, computational methods, applications, examples and exercises, and an appendix on the work of E.H. Moore.
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.
The authors contributed to the theory, computation and applications of generalized inverses, and did much to popularize the field in the first edition.
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5 of 9 people found the following review helpful:
5.0 out of 5 stars
An excellent book,
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This review is from: Generalized inverses: Theory and applications
This book is well-written and the authors explain the relationship among generalized inverses very clearly, unlike some other books.
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Inside This Book
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First Sentence:
It is well known that every non singular matrix A has a unique inverse, denoted by A-1, such that AA-1=A-1A = I, (1) where I is the identity matrix. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
multiplicative matrix norm, diagonable matrices, decomposable with respect, spectral inverses, principal idempotents, same null space, partial isometrics, rank factorization, group inverse, partial isometry, generalized inverses, inverse graph, convex norms, efficient characterization, linear operator equations, normal matrices, idempotent matrices, orthogonal projector, gauge function, principal angles, extremal solution, parallel sum, case the general solution, spectral norm, partial isometries Key Phrases - Capitalized Phrases (CAPs): (learn more)
Moore Penrose, Suggested Further Reading, Van Loan, Use Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
It is well known that every non singular matrix A has a unique inverse, denoted by A-1, such that AA-1=A-1A = I, (1) where I is the identity matrix. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
multiplicative matrix norm, diagonable matrices, decomposable with respect, spectral inverses, principal idempotents, same null space, partial isometrics, rank factorization, group inverse, partial isometry, generalized inverses, inverse graph, convex norms, efficient characterization, linear operator equations, normal matrices, idempotent matrices, orthogonal projector, gauge function, principal angles, extremal solution, parallel sum, case the general solution, spectral norm, partial isometries Key Phrases - Capitalized Phrases (CAPs): (learn more)
Moore Penrose, Suggested Further Reading, Van Loan, Use Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 77
books:
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86
books
cite this book:
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- Linear Algebra by Michael Ed. Hill on 4 pages
- Linear Algebra (Electronic Companions) by David Carlson in Back Matter (1), and Back Matter (2)
- The Algebra of Random Variables (Probability & Mathematical Statistics) by Melvin D. Springer in Back Matter
- Functional Analysis by L. V. Kantorovich in Back Matter
- Linear Algebra: Supplementary Notes & Problems by E. L. Cohen in Back Matter
See all 77 books this book cites
- Theory of Generalized Inverses Over Commutative Rings (Algebra, Logic and Applications) by K.P.S. Bhaskara Rao in Back Matter (1), and Back Matter (2)
- Mathematical Analysis of Spectral Orthogonality (Practical Spectroscopy) by John Kalivas on page 175, and Back Matter
- Matrix Algebra for Applied Economics by Shayle R. Searle on page 203, and Back Matter
- Matrix Algebra Useful for Statistics (Wiley Series in Probability and Statistics) by Shayle R. Searle on page 212, and Back Matter
- Multicomponent Flow Modeling (Modeling and Simulation in Science, Engineering and Technology) by Vincent Giovangigli on page 190, and page 299
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