行块矩阵M-P逆的充要条件

The Necessary and Sufficient Conditions for the M-P Inverse for a Row Block Matrix

通过使用矩阵秩方法,证明了如下结果:[A,B]+=[αA+βB+]βAA*αBB*.[A,B][A,B]+=αAA++βBB+R(A)=R(B).这里,α+β=1,α>0,β>0.这两个结果是2007年田永革在国际线性代数学会会刊中获得的相应结果的推广.

Through the matrix rank method, this note prove that the following results：[A,B]^＋=[αA^＋/βB^＋]←→βAA^＊=αBB^＊.[A,B][A,B]^＋=αAA^＋＋βBB^＋←→A（A）=A（B）.where α＋β=1,α〉0,β〉0.These two results are the generalization of eorespongding results of Tian [3].