分块矩阵加权广义逆的Banachiewicz-Schur形式

The Weighted Generalized Inverses of Block Matrices in Banachiewicz-Schur Form

本文主要给出了分块矩阵的加权广义逆P(1,3M),P(1,4N)与其相对应的加权广义逆的Banachiewicz-Schur形式相等的证明。利用二者之差的秩等于零证明了该形式的存在性,以及二者相等时的充要条件。

The conditions under which the weighted generalized inversesP（1,3M） and P（1,4N） can be expressed in Banachiewicz-Schur form are given in this paper. The existence of this form is proved by means of making a differ- ence of the two formulas which is 0, as well as the necessary and sufficient conditions when these two are equal.