Abstract
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.
Similar content being viewed by others
References
Baksalary, O.M., Trenkler, G.: Core inverse of matrices. Linear Multilinear Algebra 58, 681–697 (2010)
Baksalary, O.M., Trenkler, G.: On a generalized core inverse. Appl. Math. Comput. 236, 450–457 (2014)
Ben-Israel, A., Greville, T.N.E.: Generalized Inverses: Theory and Applications, 2nd edn. Springer, Berlin (2003)
Campbell, S.L., Meyer, C.D.: Generalized Inverses of Linear Transformations. SIAM, Bangkok (2009)
de Andrade, B.J.: A note on the product of two matrices of index one. Linear Multilinear Algebra 65(7), 1479–1492 (2017)
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
Hartwig, R.E., Spindelböck, K.: Matrices for which \(A^{\ast } \) and \(A^{ }\) commute. Linear Multilinear Algebra 14(3), 241–256 (1984)
Li, T., Chen, J.: Characterizations of core and dual core inverses in rings with involution. Linear Multilinear Algebra 66(4), 717–730 (2018)
Malik, S.B., Rueda, L., Thome, N.: The class of \(m\)-EP and \(m\)-normal matrices. Linear Multilinear Algebra 64(11), 2119–2132 (2016)
Malik, S.B., Thome, N.: On a new generalized inverse for matrices of an arbitrary index. Appl. Math. Comput. 226, 575–580 (2014)
Manjunatha Prasad, K., Mohana, K.S.: Core-EP inverse. Linear Multilinear Algebra 62(6), 792–802 (2014)
Meenakshi, A.R., Krishnamoorthy, S.: On \(k\)-EP matrices. Linear Algebra Appl. 269(1–3), 219–232 (1998)
Mehdipour, M., Salemi, A.: On a new generalized inverse of matrices. Linear Multilinear Algebra 66(5), 1046–1053 (2018)
Mosić, D.: The CMP inverse for rectangular matrices. Aequ. Math. 92, 649–659 (2018)
Pearl, M.H.: On generalized inverses of matrices. Math. Proc. Camb. Philos. Soc. 62, 673–677 (1966)
Tian, Y.: How to characterize commutativity equalities for Drazin inverses of matrices. Arch. Math. 39(3), 191–199 (2003)
Tian, Y., Wang, H.: Characterizations of EP matrices and weighted-EP matrices. Linear Algebra Appl. 434(5), 1295–1318 (2011)
Wang, H., Liu, X.: Characterizations of the core inverse and the core partial ordering. Linear Multilinear Algebra 63(9), 1829–1836 (2015)
Wang, H.: Core-EP decomposition and its applications. Linear Algebra Appl. 508, 289–300 (2016)
Wang, H., Chen, J.: Weak group inverse. Open Math. 16, 1218–1232 (2018)
Xu, S., Chen, J., Zhang, X.: New characterizations for core inverses in rings with involution. Front. Math. China 12(1), 231–246 (2017)
Zhang, F.: Matrix Theory: Basic Results and Techniques. Springer, Berlin (2011)
Funding
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 **aoji 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.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
All authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wang, H., Liu, X. The weak group matrix. Aequat. Math. 93, 1261–1273 (2019). https://doi.org/10.1007/s00010-019-00639-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00010-019-00639-8