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; 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.
Audience: This book is intended for use as a reference by applied scientists and engineers.
Contents: Preface to the Classics Edition; Preface; Chapter 0: Introduction and other preliminaries; Chapter 1: The Moore-Penrose or generalized inverse; Chapter 2: Least squares solutions; Chapter 3: Sums, partitioned matrices and the constrained generalized inverse; Chapter 4: Partial isometries and EP matrices; Chapter 5: The generalized inverse in electrical engineering; Chapter 6: (i, j, k)-Generalized inverses and linear estimation; Chapter 7: The Drazin inverse; Chapter 8: Applications of the Drazin inverse to the theory of finite Markov chains; Chapter 9: Applications of the Drazin inverse; Chapter 10: Continuity of the generalized inverse; Chapter 11: Linear programming; Chapter 12: Computational concerns; Bibliography; Index
Author(s): Stephen L. Campbell, Carl D. Meyer
Series: Classics in Applied Mathematics
Publisher: Society for Industrial and Applied Mathematics
Year: 2008
Language: English
Pages: 292
Tags: Математика;Линейная алгебра и аналитическая геометрия;Линейная алгебра;
Contents ......Page 11
Preface to the Classics Edition ......Page 15
Preface ......Page 21
0 Introduction and other preliminaries ......Page 23
1 The Moore-Penrose or generalized inverse ......Page 30
2 Least squares solutions ......Page 50
3 Sums, partitioned matrices and the constrained generalized inverse ......Page 68
4 Partial isometries and EP matrices ......Page 93
5 The generalized inverse in electrical engineering ......Page 99
6 (i,j,k)-generalized inverses and linear estimation ......Page 113
7 The Drazin inverse ......Page 142
8 Applications of the Drazin inverse to the theory of finite Markov chains ......Page 173
9 Applications of the Drazin inverse ......Page 193
10 Continuity of the generalized inverse ......Page 232
11 Linear programming ......Page 258
12 Computational concerns ......Page 268
Bibliography ......Page 285
Index ......Page 291
