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

作　　者：吴炎[1] 汪际和[1] 汪文彬[2] 

机构地区：[1]琼州学院数学系,海南五指山572200 [2]琼州学院计算机科学与技术系,海南五指山572200

出　　处：《纺织高校基础科学学报》2009年第2期135-140,共6页Basic Sciences Journal of Textile Universities

基　　金：海南省教育厅高校科研资助项目(HjKj200733)

摘　　要：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.

关 键 词：幂等矩阵 相似变换 广义逆 

分 类 号：O152.1[理学—数学]