两个矩阵之和的Drazin逆的表示

Representations for Drazin Inverses of Sum of Two Matrices

考虑两个矩阵之和的Drazin逆的表示,对于n阶矩阵A,B,在A^DB=0,AB^D=0,B~πABAA~π=0,B~πAB^2 A~π=0的条件下,利用矩阵的核心幂零分解给出A+B的Drazin逆的表达式.

We considered representations for Drazin inverses of the sum of two matrices,under the condition of A^DB=0,AB^D=0,BπABAAπ=0,B^πAB^2 A^π=0for the n order matrix Aand B.We gave representations for Drazin inverses of A＋Bby using the core-nilpotent decomposition of matrices.