Version 1
: Received: 24 October 2023 / Approved: 24 October 2023 / Online: 25 October 2023 (16:12:36 CEST)
How to cite:
Tian, Y. Equalities for Mixed Operations of Moore–Penrose and Group Inverses of a Matrix. Preprints2023, 2023101669. https://doi.org/10.20944/preprints202310.1669.v1
Tian, Y. Equalities for Mixed Operations of Moore–Penrose and Group Inverses of a Matrix. Preprints 2023, 2023101669. https://doi.org/10.20944/preprints202310.1669.v1
Tian, Y. Equalities for Mixed Operations of Moore–Penrose and Group Inverses of a Matrix. Preprints2023, 2023101669. https://doi.org/10.20944/preprints202310.1669.v1
APA Style
Tian, Y. (2023). Equalities for Mixed Operations of Moore–Penrose and Group Inverses of a Matrix. Preprints. https://doi.org/10.20944/preprints202310.1669.v1
Chicago/Turabian Style
Tian, Y. 2023 "Equalities for Mixed Operations of Moore–Penrose and Group Inverses of a Matrix" Preprints. https://doi.org/10.20944/preprints202310.1669.v1
Abstract
This article shows how to establish expansion formulas for calculating the mixed operations $(A^{\dag})^{\#}$, $(A^{\#})^{\dag}$, $((A^{\dag})^{\#})^{\dag}$, $((A^{\#})^{\dag})^{\#}$, $\ldots$ of generalized inverses, where $(\cdot)^{\dag}$ denotes the Moore--Penrose inverse of a matrix and $(\cdot)^{\#}$ denotes the group inverse of a square matrix. As applications of the formulas obtained, the author constructs and classifies some groups of matrix equalities involving the above mixed operations, and derives necessary and sufficient conditions for them to hold.
Keywords
group inverse; matrix equality; Moore--Penrose inverse; range; rank
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
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.
