Remarks on Hua’s matrix equality involving generalized inverses

Abstract

In this note, some necessary and sufficient conditions for Hua’s matrix equality involving generalized inverses to hold are presented.

Keywords:

• Hua’s matrix equality
• g-inverse
• rank of Schur complement

AMS Subject Classifications::

• 15A09
• 15A24

Acknowledgements

The authors wish to thank an anonymous referee and the handling editor for their helpful suggestions and constructive comments on earlier versions of this article. This research was supported by the grants from the PhD Programs Foundation of Ministry of Education of China (20093108110001), the Scientific Research Innovation Foundation of Shanghai Municipal Education Commission (09YZ13), Natural Science Foundation of China (60672160), Singapore MoE Tier 1 Research Grant RG60/07 and Shanghai Leading Academic Discipline Project (J50101).