The $W$-weighted $m$-weak core inverse
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917619007750144 |
|---|---|
| author | Ferreyra, D. E. Mosic, D. |
| author_facet | Ferreyra, D. E. Mosic, D. |
| contents | Recently, Malik and Ferreyra introduced the $m$-weak core inverse for complex square matrices which generalizes the core-EP inverse, the WC inverse, and therefore the core inverse. The main aim of this paper is to extend the concept of $m$-weak core inverse for complex rectangular matrices. This extension is called the $W$-weighted $m$-weak core inverse. We analyse its existence and uniqueness as solution of a system of matrix equations. We present various properties, representations and characterizations of the $W$-weighted $m$-weak core inverse, as well as its applications in solving certain matrix systems. A canonical form of the $W$-weighted $m$-weak core inverse is also provided by using a simultaneous unitary block upper triangularization of a pair of rectangular matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14196 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $W$-weighted $m$-weak core inverse Ferreyra, D. E. Mosic, D. Rings and Algebras 15A09, 15A10, 15A24, 15A30 Recently, Malik and Ferreyra introduced the $m$-weak core inverse for complex square matrices which generalizes the core-EP inverse, the WC inverse, and therefore the core inverse. The main aim of this paper is to extend the concept of $m$-weak core inverse for complex rectangular matrices. This extension is called the $W$-weighted $m$-weak core inverse. We analyse its existence and uniqueness as solution of a system of matrix equations. We present various properties, representations and characterizations of the $W$-weighted $m$-weak core inverse, as well as its applications in solving certain matrix systems. A canonical form of the $W$-weighted $m$-weak core inverse is also provided by using a simultaneous unitary block upper triangularization of a pair of rectangular matrices. |
| title | The $W$-weighted $m$-weak core inverse |
| topic | Rings and Algebras 15A09, 15A10, 15A24, 15A30 |
| url | https://arxiv.org/abs/2403.14196 |