矩阵之和Drazin逆的表示及其应用  

The Representations for the Drazin Inverse of the Sum of Matrices and Its Application

作　　者：杨晓英[1] YANG Xiaoying(College of Humanities,Sichuan Information Technology College,Guangyuan 628017,China)

机构地区：[1]四川信息职业技术学院人文学院,四川广元628017

出　　处：《贵州大学学报（自然科学版）》2023年第6期13-17,23,共6页Journal of Guizhou University:Natural Sciences

基　　金：四川信息职业技术学院数学应用研究中心项目(2023KC15)。

摘　　要：通过将矩阵之和转化为矩阵之积的思想,利用矩阵Drazin逆的定义、性质,将和矩阵Drazin逆问题转化为三角分块矩阵的Drazin逆问题,给出了在一定条件下和矩阵Drazin逆新的表示,进而给出分块矩阵在更弱条件下Drazin逆的表示,最后通过算例来验证结果的科学性。Through the idea of transforming the sum of matrices into the product of matrices,and using the definition and properties of the Drazin inverse of matrix,the problem of the Drazin inverse of the sum of matrices is transformed into the problem of the Drazin inverse of triangular block matrix,and a new representation for the Drazin inverse of the sum of two matrices under certain conditions is given.Then an expression for the Drazin inverse of the block matrix under weaker conditions is given,and finally the scientificity of the result is verified by an example.

关 键 词：矩阵和 DRAZIN逆 三角矩阵 分块矩阵 

分 类 号：O151.21[理学—数学]