关于复数矩阵的强-Drazin逆  

On Strongly Drazin Inverse of Complex Matrices

作　　者：张维玺 郭世乐 陈焕艮[1] ZHANG Weixi;GUO Shile;CHEN Huanyin(School of Science,Hangzhou Normal University,Hangzhou 311121,China;School of Electronics and Information Engineering,Fujian Polytechnic Normal University,Fuqing 350300,China)

机构地区：[1]杭州师范大学理学院,浙江杭州311121 [2]福建技术师范学院电子与信息工程学院,福建福清350300

出　　处：《杭州师范大学学报（自然科学版）》2020年第6期625-629,共5页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：浙江省自然科学基金项目(LY17A010018);福建省中青年教师教育科研项目(JA15570).

摘　　要：一个复数矩阵A∈C n×n有强-Drazin逆,如果存在复数矩阵X∈C n×n满足X 2A=X,AX=XA,A-AX∈N(C n×n).这里矩阵X是唯一的,并且称为复数矩阵A∈C n×n的强-Drazin逆.若复数矩阵P和Q都有强-Drazin逆,证明在条件PQ i P=0,i=1,2,…,n下P+Q有强-Drazin逆.文章将该结论推广到一些分块矩阵上,并举例予以说明.A complex matrix A∈C n×n has strongly Drazin,in case there is a complex matrix X∈C n×n satisfying X 2 A=X,AX=XA,A-AX∈N(C n×n).Here X shall be unique,and is called the strongly Drazin inverse of A∈C n×n.If the complex matrices P and Q both have strongly Drazin inverses,it is proved that P+Q has strongly Drazin inverse if PQ i P=0 and i=1,2,…,n.The study generalizes the preceding theorem to some block matrices,and gives examples to illustrate the results.

关 键 词：强-Drazin逆 加性结果 分块矩阵 

分 类 号：O153.3[理学—数学]