一类矩阵的Drazin逆

A Class Drazin Inverse of Matrix

本文得到了一类环上矩阵Ｄｒａｚｉｎ逆的一个定理：设Ｎ表有单位元环Ｒ中零元、可逆元集合与Ｒ的中心Ｚ（Ｒ）的交集，Ｍ表Ｒ的子域与Ｚ（Ｒ）的交集，Ａ∈Ｒｎ×ｎ．若ｆ（λ）＝ｃλｋ（１－λｑ（λ））是Ａ的化零多项式，其中ｑ（λ）的系数属于Ｎ，且ｃ∈Ｎ，则Ａ的Ｄｒａｚｉｎ逆存在，且Ｘ＝Ａｋ［ｑ（Ａ）］ｋ＋１是Ａ的唯一的一个Ｄｒａｚｉｎ逆．

This article gives a theorem of a class Drazin Invese of matrix over ring: If N represent a meet of zero element、 invertible element and center Z(R) of ring R with unit element, M represent a meet of subfield and center Z(R) of R, A∈Rn×m. Assume f(λ)=cλk polynomial of reduce zero, here q(λ) coefficient attribute to N and c∈N, then A Drazin Inverse is existence and X=Akk+1 is unique Drazin Inverse of A.