@article{Gao2023, 
author = {Jiale Gao and Kezheng Zuo and Qingwen Wang and Jiabao Wu},
title = {Further characterizations and representations of the Minkowski inverse in Minkowski space},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {23403-23426},
keywords = {Minkowski inverse, Minkowski space, Hartwig-Spindelböck decomposition, full-rank factorization},
url = {https://www.sciopen.com/article/10.3934/math.20231189},
doi = {10.3934/math.20231189},
abstract = {This paper serves to identify some new characterizations and representations of the Minkowski inverse in Minkowski space. First of all, a few representations of    {  1  ,      3                  m              }-,    {  1  ,  2  ,      3                  m              }-,    {  1  ,      4                  m              }- and    {  1  ,  2  ,      4                  m              }-inverses are given in order to represent the Minkowski inverse. Second, some famous characterizations of the Moore-Penrose inverse are extended to that of the Minkowski inverse. Third, using the Hartwig-Spindelböck decomposition, we present a representation of the Minkowski inverse. And, based on this result, an interesting characterization of the Minkowski inverse is showed by a rank equation. Finally, we obtain several new representations of the Minkowski inverse in a more general form, by which the Minkowski inverse of a class of block matrices is given.}
}