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