α- chain Diagonally Dominant Matrix and Criterion for Nonsingular H-matrix

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.