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

Abstract

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.

Keywords:

• Moore–Penrose inverse
• nonnegativity
• a dominance rule

AMS Subject Classification:

• 15A09

Acknowledgements

The authors thank Professor Shaun Fallat and the referees for helpful suggestions and comments.