中文摘要：

设A=（aij）∈Cn×n,若存在α∈（0,1）,使i∈N,aii≥Rαi（A）S1i-α（A）,则称A为α-链对角占优矩阵。利用α-链对角占优矩阵、不可约α-链对角占优矩阵、广义α-链对角占优矩阵等概念及性质,给出了非奇异H-矩阵几个简洁的判定条件。进一步丰富和完善了α-链对角占优矩阵与判别非奇异H-矩阵的理论,为相关领域如矩阵论、控制论、经济数学等提供了理论研究基础。

英文摘要：

Let A = （ aij） ∈ Cn×n ,if there exists α ∈ （ 0,1） which can make aii ≥ Rαi （ A） S1i -α（ A） be right for ■i ∈ N = { 1,2,…,n} ,then A is called a α-chain diagonally dominant matrix. By using concepts and properties of the α-chain diagonally dominant matrices; irreducible α-chain diagonally dominant matrices and generalized strictly α-chain diagonally dominant matrices,several sufficient conditions for a matrix to be a nonsingular H-matrix were given. Improving and completing the theory of α- chain diagonally dominant matrix and H -matrix,providing theory’s base for relative fields,such as in matrix theory,control theory,mathematical economics and so on.