Representations of the weighted WG inverse and a rank equation's solution

Abstract

In this paper, we present several representations of the W-weighted WG inverse. These representations are expressed in terms of matrix powers as well as in terms of matrix products involving only the Moore–Penrose inverse. In addition, a new characterization of the W-weighted WG inverse is presented by using a rank equation.

Keywords:

• Generalized inverse
• W-weighted WG inverse
• weighted core EP inverse
• W-weighted Drazin inverse
• rank equation

AMS Classification:

• 15A09

Acknowledgments

The authors would like to thank the anonymous referees for their impressive work and for many valuable comments and suggestions that helped them to improve the readability and organization of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author was partially supported by Universidad Nacional de Río Cuarto (Grant PPI 18/C559), CONICET (Grant PIP 112-201501-00433CO), Universidad Nacional de La Pampa, Facultad de Ingeniería (Grant Resol. Nro. 135/19), and by ANPCyT (Grant PICT 2018-03492). The second author was partially supported by Universidad Nacional de Río Cuarto (Grant PPI 18/C559). The third author was partially supported by Universidad Nacional de La Pampa, Facultad de Ingeniería (Grant Resol. Nro. 135/19), by Ministerio de Economía y Competitividad of Spain (grant DGI MTM2017-90682-REDT), and by Universidad Nacional de Río Cuarto (Grant Res. 083/2020).