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Left and right G-outer inverses.
- Source :
-
Linear & Multilinear Algebra . Nov2022, Vol. 70 Issue 17, p3319-3344. 26p. - Publication Year :
- 2022
-
Abstract
- The main contribution of this paper is to present new generalized inverses as weaker versions of a G-outer inverse. In particular, we define and characterize left and right G-outer inverses of rectangular matrices. Solvability of matrix equation systems as AXA = AEA and BAEAX = B; or AXA = AEA and XAEAD = D, where A ∈ C m × n , B ∈ C p × m , D ∈ C n × q and E ∈ C n × m , is studied by means of left and right G-outer inverses. The general solution forms of these systems give descriptions of the sets of all left and right G-outer inverses. Using left and right G-outer inverses, we introduce new partial orders and establish their relations with minus partial order and space pre-order. We apply these results to present and investigate left and right G-Drazin inverses of square matrices and corresponding partial orders. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MATRIX inversion
Subjects
Details
- Language :
- English
- ISSN :
- 03081087
- Volume :
- 70
- Issue :
- 17
- Database :
- Academic Search Index
- Journal :
- Linear & Multilinear Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 160114177
- Full Text :
- https://doi.org/10.1080/03081087.2020.1837062