The $W$-weighted $m$-weak core inverse
Abstract
Recently, Malik and Ferreyra introduced the -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 -weak core inverse for complex rectangular matrices. This extension is called the -weighted -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 -weighted -weak core inverse, as well as its applications in solving certain matrix systems. A canonical form of the -weighted -weak core inverse is also provided by using a simultaneous unitary block upper triangularization of a pair of rectangular matrices.
Keywords
Cite
@article{arxiv.2403.14196,
title = {The $W$-weighted $m$-weak core inverse},
author = {D. E. Ferreyra and D. Mosic},
journal= {arXiv preprint arXiv:2403.14196},
year = {2024}
}