GDMP-inverses of a matrix and their duals

ABSTRACT

This paper introduces and investigates a new class of generalized inverses, called GDMP-inverses (and their duals), as a generalization of DMP-inverses. GDMP-inverses are defined from G-Drazin inverses and the Moore-Penrose inverse of a complex square matrix. In contrast to most other generalized inverses, GDMP-inverses are not only outer inverses but also inner inverses. Characterizations and representations of GDMP-inverses are obtained by means of the core-nilpotent and the Hartwig-Spindelböck decompositions.

Keywords:

• Generalized inverse
• Moore-Penrose inverse
• matrix equation
• G-Drazin inverse

AMS Subject Classifications:

• 15A09
• 15A24

Acknowledgments

We would like to thank the Referees for their valuable comments and suggestions which helped us to improve the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Partially supported by Universidad Nacional de La Pampa, Facultad de Ingeniería (grant Resol. Nro. 135/19). Partially supported by Ministerio de Economía, Industria y Competitividad of Spain (Grant Red de Excelencia MTM2017-90682-REDT). Secretaría de Estado de Investigación, Desarrollo e Innovación