局部环上幂等矩阵线性组合广义逆之间的关系

The relationship between generalized inverse of linear combinations of idempotent matrices over a local ring

设R是2为单位的局部环.研究了R上三个两两可换的n阶非零幂等矩阵的线性组合广义逆之间的包含关系,确定了R上一类特殊矩阵广义逆的列表算法.利用这种列表算法和相关的矩阵理论,得到了这些矩阵线性组合广义逆之间的包含关系的充要条件,推广了矩阵自反广义逆的逆反律的相关结果.

Let R be a local ring with 2 is an unit. In this paper, the inclusion relation of the generalized inverse of linear combinations of three nonzero n times n idempotent matrices which are mutually commutative are studied over a local ring R, and the tabulation algorithm for the generalized inverse of a class special matrix are given. Moreover,by using the tabulation algorithm and the relative matrix theory , the necessary and sufficient conditions of inclusion relationships about the generalized inverse of linear combinations of these matrices are obtained, and the relative theory of reverse order law for reflexive generalized inverse of matrix are also generalized.