关于强-Drazin逆的Cline公式  

Cline Formula of Strongly Drazin Inverse

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）》2021年第3期284-288,共5页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：浙江省自然科学基金项目(LY21A010018);福建省中青年教师教育科研项目(JA15570)。

摘　　要：对于环R中元素a,b,如果ab具有Draizn逆,那么ba就有Drazin逆.此时,(ba)D=b((ab)D)2a,称为Cline公式.文章证明了强-Drazin逆的Cline公式,获得了强-Draizn逆在若干多项式条件下的Cline公式,进而得到了复数矩阵的幂等-幂零分解新性质,并给出一些例子来说明所得结论.It is well know that for a ring R, if ab has Drazin inverse, then ba has Drazin inverse. In this case,(ba)D=b((ab)D)2a is called Cline formula. This note proves the Cline formula of strongly Drazin inverse, gets the Cline formula of strongly Drazin inverse under several polynomial conditions, and further obtains the new property of idempotent-zero decomposition of complex matrix. Finally, the paper gives some examples to illustrate the results.

关 键 词：强-Drazin逆 Cline公式 环上矩阵 

分 类 号：O153.3[理学—数学]