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Solving an open problem about the G-Drazin partial order

Ferreyra, David Eduardo et al · International Linear Algebra Society · 2020

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Author / responsible party
Ferreyra, David Eduardo et al
Publisher
International Linear Algebra Society
Year
2020
ISSN
1081-3810
ISSN
1081-3810
Language
English

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G-Drazin inverses and the G-Drazin partial order for square matrices have been both recently introduced by Wang and Liu. They proved the following implication: If A is below B under the G-Drazin partial order, then any G-Drazin inverse of B is also a G-Drazin inverse of A. However, this necessary condition could not be stated as a characterization and the validity (or not) of the converse implication was posed as an open problem. In this paper, this problem is completely solved. It is obtained that the converse, in general, is false, and a form to construct counterexamples is provided. It is also proved that the converse holds under an additional condition (which is also necessary) as well as for some special cases of matrices. Fil: Ferreyra, David Eduardo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina Fil: Lattanzi, Marina Beatriz. Universidad Nacional de la Pampa. Facultad de Cs.exactas y Naturales. Dto de Matemática; Argentina

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APA 7

Ferreyra, D. E. E. A. (2020). Solving an open problem about the G-Drazin partial order. http://hdl.handle.net/11336/132022

MLA

Ferreyra, David Eduardo et al. "Solving an open problem about the G-Drazin partial order." 2020. http://hdl.handle.net/11336/132022.

Chicago

Ferreyra, David Eduardo et al. 2020. "Solving an open problem about the G-Drazin partial order.". http://hdl.handle.net/11336/132022.

Harvard

Ferreyra, D. E. E. A. 2020, Solving an open problem about the G-Drazin partial order, International Linear Algebra Society, available at: http://hdl.handle.net/11336/132022 [Accessed 9 Aug. 2026].

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Title
Solving an open problem about the G-Drazin partial order
Author / contributors
Ferreyra, David Eduardo et al
Publisher
International Linear Algebra Society
Publication year
2020
ISSN
1081-3810
ISSN
1081-3810
Language
English

Subjects

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G-DRAZIN INVERSE; G-DRAZIN PARTIAL ORDER; MINUS PARTIAL ORDER; SPACE PRE-ORDER; https://purl.org/becyt/ford/1.1; https://purl.org/becyt/ford/1
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