群逆和Drazin逆的一种新的表达式及其应用  

NEW REPRESENTATIONS FOR GROUP INVERSE AND DRAZIN INVERSE WITH THEIR APPLICATIONS

作　　者：蔡静[1] 

机构地区：[1]湖州师范学院理学院,浙江湖州313000

出　　处：《数学杂志》2009年第1期66-72,共7页Journal of Mathematics

基　　金：浙江省自然科学基金项目(Y604127);浙江省教育厅科研项目(20060315)

摘　　要：本文研究了群逆的存在条件及群逆、Drazin逆的表示与计算.利用行列式表示方法,得到了群逆存在的充要条件,给出了群逆的与原矩阵最大非奇异子阵有关的表达式.并推广到Drazin逆.为群逆和Drazin逆的计算提供了一类新的算法.In this paper, we study the condition for the existence of group inverse, representations of group inverse and Drazin inverse and their computations. A sufficient and necessary condition for the existence of group inverse is given by means of determinantal representation. New representation of group inverse is also presented in terms of original matrix＇s maximal nonsingular submatrix. Based on this, we generalize the results to Drazin inverse. Thus we propose a new method to calculate group inverse and Drazin inverse.

关 键 词：群逆 DRAZIN逆 复合矩阵 最大非奇异子阵 

分 类 号：O151.21[理学—数学]