超广义k次投影的线性组合群可逆和可逆性

The Invertibility and Group Inverse of a Linear Combination of Hyper Generalized K-projectors

在T_2T_1T_1~#=T_1T_2^(k+1)、T_2T_1=T_1T_2=T_1T_2^(k+1)及T_1T_2T_1=T_2T_1等条件下给出了超广义k次投影的线性组合群可逆的表示。利用群可逆矩阵的分解,讨论两个超广义k次投影线性组合c1T_1±c2T_2的群可逆,并且在某些条件下给出表达式。同时,研究c1T_1±c2T_2的非奇异性。在条件T_1^(k+1)T_2=T_2^(k+1)T_1下,考虑了超广义k次投影线性组合的可逆性。

In this paper, a representation of groupinverse of a linear combinationof hyper generalized k-projectorswasgiven under these conditions, such as T2T1T1^#=T1T2^k＋1、T2T1=T1T2=T1T2^k＋1、T1T2T1=T2T1and so on. The group inverse of linearcombination of two hyper generalized k-projectors c1T1±c2T2 was discussed by using thedecomposition of group inverlible matrix, and under some conditions,the expressions weregiven. Meanwhile, thenonsingulafity ofc1T1±c2T2 was studied. Finally, under the condition T1^k＋1T2=T2^k＋1T1,the invertibility tor a linearcombination of hyper generalized k-projectors is considered.