Criteria of Generalized α-Doubly Diagonally Dominant Matrices

Let A=(aij)∈Cn×n,[WTBZ]if there exists α∈(0,1),which can make |aiiajj|≥(RiRj)α(SiSj)1-α be right for i≠j(i,j∈N={1,2,…,n}),then A is called an α-doubly diagonally dominant matrix.First it is extended the concept to generalized α-doubly diagonally dominant matrix,and obtained a new necessary and sufficient condition for A to be generalized α-doubly diagonally dominant matrices,improving and generalizing the related results.This result enriches and improves the theory of α-doubly diagonally dominant matrices.