MP弱Core逆的性质和应用  

The Proper ties and Applica tions of the MP Weak Core Inverse

作　　者：刘晓冀[1] 廖梦月 靳宏伟[1] Liu Xiaoji;Liao Mengyue;Jin Hongwei(School of Mathematics and Physics,Guangxi Minzu University,Nanning 530006)

机构地区：[1]广西民族大学数学与物理学院,南宁530006

出　　处：《数学物理学报（A辑）》2022年第6期1619-1632,共14页Acta Mathematica Scientia

基　　金：国家自然科学基金(12061015);广西自然科学基金(2018GXNSFDA281023);广西科技基地与人才专项基金(桂科AD21220024)。

摘　　要：基于Moore-Penrose逆和弱Core逆该文提出了Moore-Penrose弱Core逆(MPWC逆)的概念.分别从代数和几何角度对它进行刻画,给出了MPWC逆与非奇异加边矩阵之间的关系,应用Hartwig-Spindelbock分解和Core-EP分解给出了MPWC逆的性质、刻画及其扰动分析,最后给出了矩阵的MPWC逆是EP矩阵的等价条件.In this paper,the concept of the Moore-Penrose weak Core inverse(MPWC inverse)is proposed based on the Moore-Penrose inverse and the weak Core inverse.It is described from algebraic and geometric perspectives respectively.The relationship between the MP weak Core inverse and the nonsingular bordered matrix is given.The expression of the MP weak Core inverse is given by using the Hartwig-Spindelbock decomposition and the Core-EP decomposition.The equivalence between the MP weak Core inverse of a matrix and EP matrix,the characterization and the perturbation analysis are given.

关 键 词：弱Core逆 MOORE-PENROSE逆 MPWC逆 Core-EP分解 

分 类 号：O151[理学—数学]