【摘要】 利用矩阵的秩方法,定义Bd,W2*Ad,W1 =Bd,W2W2W1Ad,W1,给出了加权Drazin逆乘积等式(^A^B)d,I=Bd,W2*Ad,W1成立的一个充分必要条件。特别,当A和B都是方阵并且W1 和W2 都是单位矩阵时,由上述结果可以直接得到Drazin逆反序律(AB)d=BdAd成立的一个充分必要条件。更多还原

【Abstract】 Recently, the reverse order laws for the generalized inverse of matrix were widely studied. Let B_d,W2*A_d,W1=B_d,W2W₂W₁A_d,W1. By using the rank methods of matrix, a necessary and sufficient condition is given for （）_d,I=B_d,W2*A_d,W1 to hold for the weighted Drazin inverse. Particularly, as A and B are square matrices, and W₁ and W₂ are identity matrices, a necessary and sufficient condition can be obtained directly for （AB）_d=B_dA_d to hold for the Drazin inverse.更多还原