English

Further properties and representations of the W-weighted m-weak group inverse

Rings and Algebras 2025-03-14 v2 Functional Analysis

Abstract

The purpose of this paper is to explore more properties and representations of the W-weighted m-weak group (in short, W-m-WG) inverse. We first explore an interesting relation between two projectors with respect to the W-m-WG inverse. Then, the W-m-WG inverse is represented by various generalized inverses including W-weighted Drazin inverse, W-weighted weak group inverse, W-weighted core inverse, etc. We also give three concise explicit expressions for the W-m-WG inverse. Moreover, a canonical form of the W-m-WG inverse is presented in terms of the singular value decomposition. Finally, several numerical examples are designed to illustrate some results given in the paper.

Keywords

Cite

@article{arxiv.2312.10704,
  title  = {Further properties and representations of the W-weighted m-weak group inverse},
  author = {Jiale Gao and Qing-Wen Wang and Kezheng Zuo},
  journal= {arXiv preprint arXiv:2312.10704},
  year   = {2025}
}

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