κ-次幂等矩阵线性组合群逆和超广义幂等矩阵线性组合Moore-Penrose广义逆的表示  

Expressions of the Group Inverse of the Linear Combinations of k-Idempotent Matrices and the Moore-Penrose Generalized Inverse of the Linear Combinations of the Hypergeneralized Idempotent Matrices

作　　者：刘晓冀[1] 张苗苗[1] BENITEZ Julio 

机构地区：[1]广西民族大学理学院,南宁530006 [2]Instituto de Matematica Multidisciplinar,Universitad Politecnica de Valencia

出　　处：《数学年刊（A辑）》2014年第4期463-478,共16页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11361009);广西省自然科学基金(No.2013GXNSFAA019008);广西教育厅重点项目(No.201202ZD031);瓦伦西亚理工大学科研项目(No.SP20120474;No.SP20120498)的资助

摘　　要：在T_1T_2T_1=T_2,T_2T_1^(k-1)=T_1T_2^(k-1)和T_1T_2T_1=T_2T_1的条件下,得到κ-次幂等矩阵线性组合群逆的表示.另外,在T_1T_2T_1=T_2和T_1~2T_2=T_2的条件下,计算超广义幂等矩阵线性组合Moore-Penrose广义逆的表示.In this paper, the expressions of the group inverse of the linear combinations of k-idempotent matrices under the conditions T1T2T1 = T2, T2 Tk1-1 = TI T2k-1 and TI T2 T1 = T2T1 are given. Moreover. The authors investigate the expressions of the Moore-Penrose generalized inverse of the linear combinations of the hypergeneralized idempotent matrices under the conditions T1T2T1 = T2 and T1 2T2 = T2.

关 键 词：线性组合 立方幂等矩阵 κ-次幂等矩阵 超广义幂等矩阵 

分 类 号：O151.21[理学—数学]