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Symmetry 2019, 11(4), 539; https://doi.org/10.3390/sym11040539

Rank Equalities Related to the Generalized Inverses A‖(B1,C1), D‖(B2,C2) of Two Matrices A and D

1
Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian 223003, China
2
Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 Valencia, Spain
*
Authors to whom correspondence should be addressed.
Received: 27 March 2019 / Revised: 9 April 2019 / Accepted: 10 April 2019 / Published: 15 April 2019
(This article belongs to the Special Issue Matrices and Symmetry)
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PDF [256 KB, uploaded 15 April 2019]

Abstract

Let A be an n × n complex matrix. The ( B , C ) -inverse A ( B , C ) of A was introduced by Drazin in 2012. For given matrices A and B, several rank equalities related to A ( B 1 , C 1 ) and B ( B 2 , C 2 ) of A and B are presented. As applications, several rank equalities related to the inverse along an element, the Moore-Penrose inverse, the Drazin inverse, the group inverse and the core inverse are obtained. View Full-Text
Keywords: Rank; (B, C)-inverse; inverse along an element Rank; (B, C)-inverse; inverse along an element
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Wang, W.; Xu, S.; Benítez, J. Rank Equalities Related to the Generalized Inverses A‖(B1,C1), D‖(B2,C2) of Two Matrices A and D. Symmetry 2019, 11, 539.

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