分块矩阵广义逆的几种表达式(英文)

Some expressions of the generalized inverses of a partitioned matrix

受分块矩阵的逆矩阵形式的启发,给出了分块矩阵A=(A_(11) A_(12) A_(21) A_(22))的广义逆A^(1,3),A^(2),A^+,A_d和A_g可以表示为x=(S_1~α-A_(11)~αA_(12) S_2~α-A_(22)~αA_(21)S_1~αS_2~α)的条件;然后运用这些结果,得到分块矩阵A的M-P逆的几个表达式;最后给出一个求分块矩阵M-P逆的例子。

We show the conditions under which the generalized inverses A^（1,3） , A^（2） , A^＋ , Ad and Ag of the partitioned matrix A = （A11 A12 A21 A22）can be expressed in the form of X = （S1^α-A11^αA12S2^α -A11^αA21S1^α S2^α）, whieh is indueed from the form of the inverse of the partitioned matrix A. Then from the results, we derive some other expressions of the Moore - Penrose inverse of the partitioned matrix A. Then from the M-P inverse of its blocks. Finally, we offer an example.