Continuity of the core-EP inverse and its applications. Issue 3 (17th February 2021)

• Record Type: Journal Article
• Authors: Gao, Yuefeng; Chen, Jianlong; Patrício, Pedro
• Is Part Of: Linear & multilinear algebra. Volume 69:Issue 3(2021)
• Page Start: 557
• Page End: 571
• Publication Date: 2021-02-17
• Subjects: Core-EP inverse -- pseudo core inverse -- continuity -- perturbation bound; 15A09 -- 34D10 -- 65F35; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2019.1608899
• Languages: English
• ISSNs: 0308-1087

Abstract

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.