Solving an open problem about the G-Drazin partial order
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 co...
| Autores: | , , , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2020 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositório: | CONICET Digital (CONICET) |
| Idioma: | inglês |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/132022 |
| Acesso em linha: | http://hdl.handle.net/11336/132022 |
| Access Level: | Acceso aberto |
| Palavra-chave: | 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 |
| Resumo: | 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. |
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