2×2分块矩阵Drazin逆的表示

The Representations of the Drazin inverse of 2×2 Matrices

给出了2×2分块矩阵M=(ABCD)在条件A3B=BD,D3C=CA,BCBD=AB和CBCA=DC下的Drazin逆的表示,其中,A,D和BC都Drazin可逆.同时也给出了其他2×2分块矩阵的Drazin逆的表示.

In this paper, we give explicit representations of the Drazin inverse of a 2 × 2 matrix M = （ABCD）under the conditions A3B=BD,D3C=CA,BCBD=AB and CBCA=DC,where A, D and BC areDrazin invertible. The representations of the Drazin inverse of other 2 ×2 matrices are also given