矩阵和的Drazin逆表示的一些结果

Some Results on the Representations for Drazin Inverses of the Sum of Two Matrices

研究两个矩阵和的Drazin逆的表示.对于n阶矩阵P,Q,在P^DQ=0,PQ^D=0,Q~πPQPP~π=0,Q~πPQ^2PP~π=0,Q~πPQ^3P~π=0的条件下,利用矩阵的核心幂零分解给出了P+Q的Drazin逆的表达式.

We give representations for Drazin inverses of the sum of two matrices P,Q ,under the condition PDQ=0,PQD=0,QπPQPPπ=0,QπPQ2PPπ=0,QπPQ3Pπ=0, the express P ＋Q of Drazin inverses is given by using the core-nilpotent decomposition of matrices and some related results are generalized.