Abstract: Let A=(a_ij)∈C^n×n, if there existsα∈(0,1) [WTBZ]which can make |a_ii|≥R^α_iS^1-α_i be right for i∈N={1,2,…,n},then  is called anα-chain diagonally dominant matrix.It gave an equivalent condition for chain strictly diagonally dominant matrices，and obtains a necessary condition for a matrix to be a nonsingular H-matrix indirectly. The result obtained improves the known corresponding results．At last, some numerical examples are given for illustrating advantages of the result.

Key words: α-Chain diagonally dominant matrix ,  Irreducible matrix ,  ,  Nonsingular H-matrix

摘要： 设A=(a_ij)∈C ^n×n ,若存在α∈(0,1),使∀i∈N ,|a_ii|≥R^α_i (A)S ^1-α _i (A),则称A 为α-链对角占优
矩阵。利用这一概念给出了α-链严格对角占优矩阵的一个充要条件,从而间接地得到了判别非奇异H -矩阵的必
要条件,改进和推广了已有的结论。最后用数值例子说明了所给结果的优越性。

关键词: &alpha, -链对角占优矩阵 ,  , 不可约矩阵,  , 非奇异H -矩阵