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Article

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

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. https://doi.org/10.3390/sym11040539

AMA Style

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(4):539. https://doi.org/10.3390/sym11040539

Chicago/Turabian Style

Wang, Wenjie, Sanzhang Xu, and Julio Benítez. 2019. "Rank Equalities Related to the Generalized Inverses A‖(B1,C1), D‖(B2,C2) of Two Matrices A and D" Symmetry 11, no. 4: 539. https://doi.org/10.3390/sym11040539

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