The weak group matrix
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In this paper,we introduce the weak group matrix defined by the one commutable with its weak group inverse, and consider properties and characterizations of the matrix by applying the core-EP decomposition. In particular,the set of weak group matrices is more inclusive than that of group matrices. We also derive some characterizations of p-EP matrices and i-EP matrices.
KeywordsWeak group matrix Group matrix p-EP matrix i-EP matrix Core-EP decomposition
Mathematics Subject Classification15A09 15A57 15A24
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This work is supported by Guangxi Natural Science Foundation [Grant Number 2018GXNSFAA138181], the China Postdoctoral Science Foundation [Grant Number 2015M581690], the National Natural Science Foundation of China [Grant Number 61772006] and the Special Fund for Bagui Scholars of Guangxi. The Xiaoji Liu was supported partially by the National Natural Science Foundation of China [Grant Number 11361009], the Special Fund for Science and Technological Bases and Talents of Guangxi [Grant Number 2016AD05050] and High level innovation teams and distinguished scholars in Guangxi Universities.
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Conflict of interest
All authors declare that they have no conflict of interest.
- 6.Ferreyra, D.E., Levis, F.E., Thome, N.: Characterizations of \(k\) commutative equalities for some outer generalized inverses. Linear Multilinear Algebra (2018). https://doi.org/10.1080/03081087.2018.1500994