局部环上两个同阶幂等矩阵及其积在同一相似变换下的广义逆

The generalized inverse of two idempotent matrices and their product under the similar transformation over a local ring

设R是一个局部环,在R上同一相似变换下将单个矩阵的广义逆理论进行推广.利用局部环上矩阵方法和同一相似变换下的矩阵标准形理论,研究了2个同阶幂等矩阵及其积的广义逆,得到了(1)2个幂等矩阵及其积在同一相似变换下的{k}-逆(k=1,3);(2)2个幂等矩阵及其积在同一相似变换下的{i,j}-逆的表达式,其中i≠j.

Let R is a local ring,the theory of the generalized inverse of one matrix is extended under the sameness similar transformation over R. By using the matrix methods and the theory of the normal form of matrix under the sameness similar transformation, the generalized inverse of two idempotent matrices and their product are dis- cussed under the sameness similar transformation over R, and the following conclusions are given that （ 1 ） { k } -inverse of two idempotent matrices and their product under the sameness similar transformation, where k = 1,3 ; （2） { i,j} -inverse of two idempotent matrices and their product under the sameness similar transformation, where i ≠j.