In this paper we mainly study the kth multi - g base index for non - powerful primitive irreducible generalized sign pattern matrices and primitive nearly reducible generalized sign pattern matrices . we obtain sharp ' upper bounds , together with complete characterization of the equality cases of the kth multi - g base index for primitive irreducible generalized sign pattern matrices and primitive nearly reducible generalized sign pattern matrices 在本文中我们研究了广义non - powerful不可约符号矩阵和几乎可约符号矩阵的广义k重基指数，得到了广义不可约符号矩阵的广义k重基指数的最好上界，以及广义几乎可约符号矩阵广义k重基指数的上界和某些达到上界的矩阵。
