Artículo
Solving an open problem about the G-Drazin partial order
Fecha de publicación:
08/02/2020
Editorial:
International Linear Algebra Society
Revista:
Electronic Journal Of Linear Algebra
ISSN:
1081-3810
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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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Articulos(CCT - CORDOBA)
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - CORDOBA
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - CORDOBA
Citación
Ferreyra, David Eduardo; Lattanzi, Marina Beatriz; Levis, Fabián Eduardo; Thome, Néstor; Solving an open problem about the G-Drazin partial order; International Linear Algebra Society; Electronic Journal Of Linear Algebra; 36; 1; 8-2-2020; 55-66
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