一类分块矩阵群逆存在性理论及表达式的研究  

Inverse Existence Theory of Chunked Matrix Groups and Representation for Group Inverse of a Class of Block Matrix

作　　者：朱文君 余新宏 周帅 张荣 Zhu Wen-jun;Yu Xin-hong;Zhou Shuai;Zhang Rong(Basic Teaching Department,Hefei university of economics,Hefei Anhui 230016;School of Finance and Mathematics,West Anhui University,Liuan Anhui 237012)

机构地区：[1]合肥经济学院基础教学部,安徽合肥230016 [2]皖西学院金融与数学学院,安徽六安237012

出　　处：《河西学院学报》2023年第2期19-24,共6页Journal of Hexi University

基　　金：安徽省自然科学重点研究项目(项目编号:KJ2021A1222);安徽省质量工程教学研究项目(项目编号:2021jyxm1211)。

摘　　要：通过构造分块矩阵在第一、第四子块组合的形式,结合矩阵投影算子和初等分解的方法给出一类分块矩阵群逆存在性的充分必要条件和具体表达式。拓展了分块矩阵群逆存在性理论,并验证了结果的可行性。By constructing the combination form of the block matrix in the first and fourth sub-blocks,combining the matrix projection operator and the method of elementary decomposition,the sufficient and necessary conditions and specific expressions of the inverse existence of a class of block matrix groups are given.The inverse existence theo⁃ry of block matrix group is extended and the practicability of the result is verified.

关 键 词：分块矩阵 广义逆 群逆 秩 

分 类 号：O151.21[理学—数学]