两个三次幂等矩阵组合的群可逆性  

Group Invertibility of Combinations of Two Tripotent Matrices

作　　者：武淑霞[1] 刘晓冀[1] 

机构地区：[1]广西民族大学数学与计算机科学学院,广西南宁530006

出　　处：《中北大学学报（自然科学版）》2012年第6期638-642,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11061005);四川省教育厅自然科学基金资助项目(10ZB02;11ZB153)

摘　　要：利用可交换的k次幂等矩阵可同时对角化的原理与矩阵可分块的方法,对两个可交换三次幂等矩阵的非线性组合进行了研究,其组合是群可逆的,同时给出了表达式.进一步得到了三次幂等矩阵的更一般的组合形式在一定条件下是群对和矩阵的所有情形,从而将已有的三次幂等矩阵线性组合的相关结论推广到了非线性组合上.By using the principle of simultaneous diagonalization of two commuting k-tripotent matrices and the method of partition of matrix, the group invertibility of the nonlinear combination of two commuting tripotent matrices was mainly discussed and the formula was got.Further,all the cases that the more generalized combination of tripotent matrices was group involutory matrix were obtained under certain conditions.So the results about the linear combinations of two tripotent matrices were extended to nonlinear combinations.

关 键 词：三次幂等矩阵 群对合矩阵 群逆 对合矩阵 组合 

分 类 号：O151[理学—数学]