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Schur补为零的2x2分块矩阵的Drazin逆

董鹏飞1,董鹏达2

(1.呼和浩特民族学院 数学系;内蒙古 呼和浩特 010051;2.内蒙古路桥有限责任公司 第四工程处,内蒙古 呼和浩特 010052)

摘要:本文分析研究了斯舒尔补S=D-CADB=0的分块矩阵

在某些条件下的Drazin逆表达式.

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关键词 :分块矩阵;Drazin逆;Schur补

中图分类号:O15文献标识码:A文章编号:1673-260X(2015)02-0274-02

1 引言

若矩阵A∈Cn×n,A的Drazin逆是满足

Ak+1X=Ak,XAX=X,AX=XA.

的矩阵X∈Cn×n,其中k是使得rank(Ak)=rank(Ak+1)的最小的非负整数,记k=Ind(A)为A的指标.

特别地,当Ind(A)=1,则称X为A的群逆,记作X=A#.若A#存在,则它是唯一的.如果A是非奇异的,则易知Ind(A)=0且AD=A-1.本文中令Aл=I-AAD.

Drazin逆的理论在许多领域有着广泛的应用,例如差分方程,统计,马尔科夫链,数值分析和控制理论等等[1-6].

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