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Generalized Inverses of Linear Transformations

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By Stephen L. Campbell and Carl D. Meyer


2009/ xx + 272 pages / Softcover / ISBN: 978-0-898716-71-9 / List Price $80.00 / SIAM Member Price $56.00 / Order Code CL56

Keywords: generalized inverses; pseudoinverses applied linear algebra

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.

This book is intended for use as a reference by applied scientists and engineers.

Preface to the Classics Edition
0. Introduction and other preliminaries;
1. The Moore-Penrose or generalized inverse;
2. Least squares solutions;
3. Sums, partitioned matrices and the constrained generalized inverse;
4. Partial isometries and EP matrices;
5. The generalized inverse in electrical engineering;
6. (i, j, k)-Generalized inverses and linear estimation;
7. The Drazin inverse;
8. Applications of the Drazin inverse to the theory of finite Markov chains;
9. Applications of the Drazin inverse;
10. Continuity of the generalized inverse;
11. Linear programming;
12. Computational concerns;

About the Authors
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.

ISBN: 9780898716719

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