Continuity of the core-EP inverse and its applications

ABSTRACT

In this paper, firstly we study the continuity of the core-EP inverse without explicit error bounds by virtue of two methods. One is the rank equality, followed from the classical generalized inverse. The other one is matrix decomposition. The continuity of the core inverse can be derived as a particular case. Secondly, we study perturbation bounds for the core-EP inverse under prescribed conditions. Perturbation bounds for the core inverse can be derived as a particular case. Also, as corollaries, the sufficient (and necessary) conditions for the continuity of the core-EP inverse are obtained. Thirdly, a numerical example is illustrated to compare derived upper bounds. Finally, an application to semistable matrices is provided.

Keywords:

• Core-EP inverse
• pseudo core inverse
• continuity
• perturbation bound

AMS Subject Classifications:

• 15A09
• 34D10
• 65F35

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by the National Natural Science Foundation of China (No. 11771076), partially supported by FCT- ‘Fundação para a Ciência e a Tecnologia’, within the project UID-MAT-00013/2013.