关于分块矩阵〔ABCD〕的g-逆的块独立性  

On the Block Independence in g-lnverse of a Matrix〔ABCD〕

作　　者：陈永林[1] 

机构地区：[1]南京师范大学,南京210024

出　　处：《应用数学》1993年第3期241-248,共8页Mathematica Applicata

基　　金：国家自然科学基金

摘　　要：本文证明了分块阵M=〔ABCD〕的g-逆有块独立性的充要条件是M适合秩可加性条件,M^+有一特定的表达式的充要条件也是M适合秩可加性条件.本文还给出了包含M的g-逆的子块的不变矩阵以及这些子块的定义方程.In this paper, we have shown a somewhat amazing fact that the rank additivity condition is necessary and sufficient for the block independence in g-inverse of a partitioned matrix M={A B C D}and for the Moore-Penrose inverse M^+ to have a particular expression. Besides, we have given some invariants involving the blocks of g-inverse of M and the definition equation of these blocks.

关 键 词：块独立性 秩可加性 分块矩阵 g逆 

分 类 号：O151.21[理学—数学]