A dominance rule for singular matrices using proper splittings is proposed. This extends the corresponding notion, known for nonsingular matrices. An application to the nonnegativity of the Moore-Penrose inverse is presented. © 2012 Copyright Taylor and Francis Group, LLC.

K C Sivakumar

Department of Mathematics

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

A dominance notion for singular matrices with applications to nonnegative generalized inverses

Linear and Multilinear Algebra

the theory and applications of iteration methods

The Electronic Journal of Linear Algebra

Additional results on index splittings for Drazin inverse solutions of singular linear systems

International Journal of Computer Mathematics

(T,S) splitting methods for computing the generalized inverse and rectangular systems∗

Springer Series in Computational Mathematics

Matrix Iterative Analysis

Applied Mathematics and Computation

Index splitting for the Drazin inverse and the singular linear system

Journal	Linear and Multilinear Algebra
ISSN	03081087
Open Access	No