A Simple Criterion for Nonsingular H-Matrix

Let A=(aij)∈Cn×n,if there exists α∈(0,1) which can make |aii|≥αRi(A)+(1-α)Si(A) be right for i∈N,then A is called a α-diagonally dominant matrix.Extend the concept to generalized α-diagonally dominant matrix,and apply the concepts and properties of α-diagonally dominant matrices,irreducible α-diagonally dominant matrices and generalized strictly α-diagonally 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 nonsingular H-matrix,but also lay a solid foundation for the research of computational mathematic,matrix theory,control theory,mathematical economics,etc.