关于矩阵广义逆符号模式的若干性质

若一个实矩阵A的广义逆A^ 的符号模式由A的符号模式所唯一确定，则A被称为广义逆符号唯一。在关于广义逆符号唯一矩阵的一些现有结论基础上，进一步研究了当矩阵A为广义逆符号唯一时，A^ 的符号模式和零位模式的具体特征。还讨论了法A不为广义逆符号唯一时，与A有相同符号模式的矩阵广义逆族在某些位置上所能取到的不同符号情况，并且给出了这一结果在讨论线性方程组的最小二乘符号可解性中的一个应用。

On Some Properties of Sign Pattern of Generalized Inverse

A real matrix A is said to have a signed generalized inverse if the sign pattern of its generalized inverse A is uniquely determined by the sign pattern of A.In this paper,on the base of researches about signed generalized inverses,we further study the sign pattern and zero pattern of A where A is a matrix having signed generalized inverse.We also apply these results to obtain some property of least spuare sign solvable linear systems in terms of matrices having signed generalized inverses.