Version 1
: Received: 3 April 2023 / Approved: 4 April 2023 / Online: 4 April 2023 (12:16:28 CEST)
How to cite:
Tian, Y. Towards Finding Equalities Involving Mixed Products of the Moore–Penrose and Group Inverses of a Matrix. Preprints2023, 2023040043. https://doi.org/10.20944/preprints202304.0043.v1
Tian, Y. Towards Finding Equalities Involving Mixed Products of the Moore–Penrose and Group Inverses of a Matrix. Preprints 2023, 2023040043. https://doi.org/10.20944/preprints202304.0043.v1
Tian, Y. Towards Finding Equalities Involving Mixed Products of the Moore–Penrose and Group Inverses of a Matrix. Preprints2023, 2023040043. https://doi.org/10.20944/preprints202304.0043.v1
APA Style
Tian, Y. (2023). Towards Finding Equalities Involving Mixed Products of the Moore–Penrose and Group Inverses of a Matrix. Preprints. https://doi.org/10.20944/preprints202304.0043.v1
Chicago/Turabian Style
Tian, Y. 2023 "Towards Finding Equalities Involving Mixed Products of the Moore–Penrose and Group Inverses of a Matrix" Preprints. https://doi.org/10.20944/preprints202304.0043.v1
Abstract
Given a square matrix $A$, we are able to construct numerous equalities that involve reasonable mixed operations of $A$ and its conjugate transpose $A^{\ast}$, Moore--Penrose inverse $A^{\dag}$, and group inverse $A^{\#}$. Such kind of equalities can be generally represented in the equation form $f(A, \, A^{\ast}, A^{\dag}, A^{\#}) =0$. In this article, the author constructs a series of simple or complicated matrix equalities, as well as matrix rank equalities involving the mixed operations of the four matrices. As applications, we give a sequence of necessary and sufficient conditions for a square matrix to be range-Hermitian.
Keywords
block matrix; group inverse; Moore--Penrose inverse; range; rank; reverse-order law
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.
