Criteria of Generalized α-doubly Diagonally Dominant Matrix

Let A=(aij)∈Cn×n,if there exists α∈(0,1),which can make aiiajj[αRi(A)+(1-α)Si×(A)][αRj(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,the concept is extend 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.Finally,two numerical examples are given for illustrating advantage of results.