The necessary and sufficient condition criterion for nonsingular H-matrix

Let A=(aij)∈Cn×n,if there exists α∈(0,1),which can make aii·ajj[αΛi(A)+(1-α)Si(A)]·[αΛj(A)+(1-α)Sj(A)]be right for i≠j(i,j∈N={1,2,…,n}),then A is called a α-doubly diagonal strictly dominant matrix.First,we extend the concept to generalized α-doubly diagonally strictly dominant matrix,and obtain a new necessary and sufficient condition for A=(aij)∈Cn×n to be generalized α-doubly diagonally dominant matrix,improving and generalizing the related results.This result enriches and improves the theory of α-doubly diagonally dominant matrix.