Generalized Inverses of Linear Transformations

by Campbell, Stephen A.; Meyer, Carl D.

• ISBN13: 9780898716719
• ISBN10: 0898716713
• Format: Paperback
• Copyright: 2009-06-30
• Publisher: Cambridge Univ Pr

Summary

Generalized (or pseudo-) inverse concepts routinely appear throughout applied mathematics and engineering, in both research literature and textbooks. Although the basic properties are readily available, some of the more subtle aspects and difficult details of the subject are not well documented or understood. This book is an excellent reference for researchers and students who need or want more than just the most basic elements. First published in 1979, the book remains up-to-date and readable, and it includes chapters on Markov chains and the Drazin inverse methods that have become significant to many problems in applied mathematics. Generalized Inverses of Linear Transformations provides comprehensive coverage of the mathematical theory of generalized inverses coupled with a wide range of important and practical applications that includes topics in electrical and computer engineering, control and optimization, computing and numerical analysis, statistical estimation, and stochastic processes.

Author Biography

Stephen L. Campbell is Professor of Mathematics and Director of Graduate Programs at North Carolina State University. His research interests include linear algebra, control theory, differential equations (especially differential algebraic equations), numerical methods, and applications. He is the author or co-author of eight books. Carl D. Meyer is Professor of Mathematics at North Carolina State University. His research interests include numerical and applied linear algebra; Markov chains and applied probability; and information retrieval, data mining, and Web search. He is the author or co-author of six books.

Table of Contents

Preface to the Classics edition

Preface

Introduction and other preliminaries

The Moore-Penrose or generalized inverse

Least squares solutions

Sums, partitioned matrices and the constrained generalized inverse

Partial isometries and EP matrices

The generalized inverse in electrical engineering

(i, j, k)-Generalized inverses and linear estimation

The Drazin inverse

Applications of the Drazin inverse to the theory of finite Markov chains

Applications of the Drazin inverse

Continuity of the generalized inverse

Linear programming

Computational concerns

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.