Let A=(a _{i j})∈ C ^{n ×n} , if the reexists α∈(0, 1)which can make a _ii ≥αRi( A)+(1 -α)S _i( A)be right for i ∈ N ,then A is called a α-diagonally dominant matrix .Ex tend the concept to generalized α-diagonally dominant matrix , and apply the concepts and proper ties of α-diagonally dominant matrices, irreducible α-diag onally dominant matrices and gene ralized strictly α-diag onally dominant matrices to obtain a simple criterion of a nonsingular H-matrix .These conclusions not only enrich and improve the theory of α-diagonally dominant matrices and nonsing ular H-matrix , but also lay a solid foundation for the research of computational mathematic , matrix theory , control theory , mathematical economics , etc .

  By using concepts and properties of the Ostrow ski diagonally dominant matrices , irreducible Ostrow ski diagonally dominant mat rices and generalized Ostrowski diagonally dominant matrices, several sufficient conditions for a nonsingular H - matrix were given .The conditions enriches the theory of Ostrow ski diagonally dominant matrices and nonsingular H -matrix , which provides theory's base for relative fields' research such as matrix theory , control theory , mathematical economics and so on .