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arXiv · 2303.13951

Further characterizations and representations of the Minkowski inverse in Minkowski space

Jiale Gao·Qingwen Wang·Kezheng Zuo·Jiabao Wu
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Abstract

This paper is aimed to identify some new characterizations and representations of the Minkowski inverse in Minkowski space. First of all, a few representations of {1,3m}, {1,2,3m}, {1,4m} and {1,2,4m}-inverses are given in order to represent the Minkowski inverse. Secondly, some famous characterizations of the Moore-Penrose inverse are extended to that of the Minkowski inverse. Thirdly, using the Hartwig-Spindelb\"ock 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.

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Jiale Gao, Qingwen Wang, Kezheng Zuo, Jiabao Wu. 2023-03-24. Further characterizations and representations of the Minkowski inverse in Minkowski space. https://arxiv.org/abs/2303.13951

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