Further characterizations and representations of the Minkowski inverse in Minkowski space

IF 1.8 3区 数学 Q1 MATHEMATICS
Jiale Gao, Qingwen Wang, Kezheng Zuo, Jiabao Wu
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引用次数: 0

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^{\mathfrak{m}}\} $-, $ \{1, 2, 3^{\mathfrak{m}}\} $-, $ \{1, 4^{\mathfrak{m}}\} $- and $ \{1, 2, 4^{\mathfrak{m}}\} $-inverses are given in order to represent the Minkowski inverse. Second, some famous characterizations of the Moore-Penrose inverse are extended to that of the Minkowski inverse. Third, using the Hartwig-Spindelböck decomposition, we present a representation of the Minkowski inverse. And, based on this result, an interesting characterization of the Minkowski inverse is showed by a rank equation. Finally, we obtain several new representations of the Minkowski inverse in a more general form, by which the Minkowski inverse of a class of block matrices is given.
闵可夫斯基逆在闵可夫斯基空间中的进一步表征与表示
本文给出了Minkowski空间中Minkowsky逆的一些新的刻画和表示。首先,为了表示Minkowski逆,给出了$\{1,3^{\mathfrak{m}}\}$-,$\{1,2,3^{\ mathfrak{m}}\}$,$\{1,2,4^{\mathfrak{m}\}$和$\{1,24,^{\mathfrak{m}}}$逆的几个表示。其次,将Moore-Penrose逆的一些著名性质推广到Minkowski逆的性质。第三,使用Hartwig-Spindelböck分解,我们给出了Minkowski逆的一个表示。在此基础上,用秩方程给出了Minkowski逆的一个有趣的性质。最后,我们以更一般的形式得到了Minkowski逆的几个新表示,并由此给出了一类块矩阵的Minkowsky逆。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
AIMS Mathematics
AIMS Mathematics Mathematics-General Mathematics
CiteScore
3.40
自引率
13.60%
发文量
769
审稿时长
90 days
期刊介绍: AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.
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