两矩阵和的Drazin逆表示

Representations of Drazin Inverse of Sum for Two Matrices

考虑两个矩阵之和的Drazin逆的表示.对于n阶矩阵P,Q,利用Cline公式及Drazin逆的性质给出在P^(2)QP^(2)=0,P^(3)QP=0,PQ 3=0,PQ^(2)P=0,P^(2)QPQ=0等条件下两矩阵和P+Q的Drazin逆的表达式.

We considered the representation of the Drazin inverses of the sum for two matrices.For n-th order matrices P and Q,the expression of the Drazin inverse of the sum for two matrices P+Q was given by using the Cline formula and the properties of Drazin inverse under the conditions such as P^(2)QP^(2)=0,P^(3)QP=0,PQ 3=0,PQ^(2)P=0,P^(2)QPQ=0,etc.