中文摘要：

设A=（nij）∈Cn×n，若存在a∈（0，1），使Vi∈N，有｜aij｜≥Ria（A）Si1-a（A）成立，则称A为a链对角占优矩阵。利用r链对角占优矩阵、不可约r链对角占优矩阵、广义严格a-链对角占优矩阵等概念及性质，给出了非奇异H-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。

英文摘要：

Let A=（nij）∈Cn×n, if there exists a∈（0,1） which can make ｜aij｜≥Ria（A）Si1-a（A） be right for Vi∈N={1,2, ..,N}, then A is called a a chain diagonally dominant matrix. By using concepts and properties of the a chain diagonally dominant matrices~ irreducible a chain diagonally dominant matrices and generalized strictly a chain diagonally dominant matrices, some sufficient conditions for a matrix to be a nonsingular H-matrix were given. The results obtained improve the known corresponding results. At last a numerical example is given for illustrating advantage of result.