Generalized inverses arise in various applications in statistics,science and engineering,shch as least squares approximation,singular differential and difference equations ,singular control,Markov chains and ill-posed problems,This book contains the latest developments in the theory and computations of generalized inverses.
This book was writter for researchers in matrix theory,numerial linear algebra,parallel computatons and,particularly,the generalized inverses with application.And it can als

Preface
List of Notations
Chapter 1 Equation Solving Generalized Inverses
1.1 The Moore-Pentose inverse
1.2 {i,j,k}inverses
1.3 The generalized inverses with prescribed range and null space
1.4 Weighted Moore-Penrose inverse
1.5 Bott-Duffin inverse and generalized Bott-Duffin inverse
Remarks on Chapter1
Chpater 2 Drazin Inverse
2.1 Drazin inverse
2.2 Group inverse
2.3 W-weighted Drazin inverse
Remarks on Chapter 2
Chapter 3 The Generalization of Cramer Rule and the Minors of the Generalized Inverses
3.1 The nonsingularity of bordered matrices
3.2 Cramer rule for the solution of a linear equation
3.3 Cramer rule for the solution of a matrix Equation
3.4 The determinantal expressions of the generalized inverses and projectors
3.5 The determinantal expressions of the minors of the generalized inverses
Remarks on Chapter 3
Chapter 4 The Reverse Order Law and Forward Order Law for the Generalized Inverses A(2)T,S
4.1 Inrroduction
4.2 Reverse order law
4.3 Forward order law
Remarks on Chapter 4
Chpater 5 Computational Aspects of the Generalized Inverses
5.1 Methods based on full rank factorizations
5.2 Singular value decompositions and (M,N)singular value decompositions
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Chapter 6 The Parallel Algorithms for Computing the Generalized Inverses
Chapter 7 Perturbation Analysis of the Moore-Penrose INverse and the Weighted Moore-Inverse
Chapter 8 Perturbation Analysis of the Drazin Inverse and the Group Inverse
Chapter 9 The Moore-Penrose Inverse of Linear Operators
Chapter 10 Drazin INverse of Operators
Chapter 11 W-weighted Drazin Inverse of Operators
References
Index