关于矩阵的外逆及矩阵的两个外逆的线性组合

ON THE OUTER INVERSES OF MATRICES AND LINEAR COMBINATIONS OF TWO OUTER INVERSES

本文研究了矩阵A的外逆的表达式,利用外逆及分块矩阵的秩的性质,得出了A的两个外逆的线性组合还是A的外逆的完全分类,不仅证明了A的两个外逆的和与差,而且A的外逆的几个充要条件,推广了Jerzy K.Baksalary和Oskar Maria Baksalary的结果.

The this paper,we research the expressions of the outer inverses of a matrix A.From the properties of rank of block matrix and outer inverses of a matrix,the classification of linear combinations of two outer inverse of A is also an outer inverses of A is obtained.Moreover,some necessary and sufficient conditions for the sum and the difference of two outer inverses of A is also an outer inverse of A are proved,which generalize the results of Jerzy K.Baksalary and Oskar Maria Baksalary.