Wang G. Generalized Inverses. Theory and Computations 2018

Textbook in PDF format

This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics.It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.
Equation Solving Generalized Inverses
Drazin Inverse
Generalization of the Cramer’s Rule and the Minors of the Generalized Inverses
Reverse Order and Forward Order Laws for A(2)T,S
Computational Aspects
Structured Matrices and Their Generalized Inverses
Parallel Algorithms for Computing the Generalized Inverses
Perturbation Analysis of the Moore-Penrose Inverse and the Weighted Moore-Penrose Inverse
Perturbation Analysis of the Drazin Inverse and the Group Inverse
Generalized Inverses of Polynomial Matrices
Moore-Penrose Inverse of Linear Operators
Operator Drazin Inverse