Abstract: Let [WTHX]A[WTBX]=(aij)∈Cn×n[WTBZ], if there exists α∈(0,1) which can make |aii|≥Rαi([WTHX]A[WTBX])S1-αi([WTHX]A[WTBZ]) be right for i∈N={1,2,…,N}, then [WTHX]A[WTBZ] is called a [WTBX]α[WTBZ] chain diagonally dominant matrix. By using concepts and properties of the [WTBX]α[WTBZ] chain diagonally dominant matrices；irreducible [WTBX]α[WTBZ] chain diagonally dominant matrices and generalized strictly [WTBX]α[WTBZ] chain diagonally dominant matrices, some sufficient conditions for a matrix to be a nonsingular [WTHX]H[WTBZ]matrix were given. The results obtained improve the known corresponding results．At last a numerical example is given for illustrating advantage of result.

Key words: matrix , Generalized strictly [WTBX]α[WTBZ] chain diagonally dominant matrix , Irreducible matrix　

摘要： 设A=(aij)暿Cn暳n,若存在毩暿(0,1),使炐i暿N,有|aii|曒R毩i (A)S1-毩i (A)成立,则称A 为毩链对角占
优矩阵。利用毩灢链对角占优矩阵、不可约毩灢链对角占优矩阵、广义严格毩灢链对角占优矩阵等概念及性质,给出了非奇
异H灢矩阵的一个简捷判别定理。从而改进和推广了相应的一些结果,并给出相应的数值例子说明结果的有效性。

关键词: 非奇异H-矩阵 , 广义严格毩-链对角占优矩阵 , 不可约矩阵