一类分块上三角阵的广义逆

Generalized inverses for a class of block triangular matrix

为了得到更为简单的分块上三角阵的广义逆的表达式,研究了分块矩阵在子矩阵T可逆的情况下一类分块上三角阵的广义逆,利用矩阵的核-EP逆、DMP逆、B-T逆和弱群逆的定义及性质给出了一类分块上三角阵的核-EP逆、DMP逆、B-T逆和弱群逆的表示定理,并利用这些表示定理,提供了另一种计算分块上三角阵的核逆的方法。

In order to obtain a more simple expression for the gereralized inverse of block triargular matrix,the block matrix is studred when the submatrix is invertible.In this paper,we give the expression theorems of the Core-EP inverse,DMP inverse,B-T inverse and weak group inverse for a class of block triangular matrix by using the definition and properties of these inverses.Furthermore,the related applications of these theorems are given.