广义α-双对角占优矩阵的判定

Criteria of Generalized α-Doubly Diagonally Dominant Matrices

设A=(aij)∈Cn×n,若存在α∈(0,1),使i≠j(i,j∈N={1,2,…,n})有|aiiajj|≥(RiRj)α(SiSj)1-α,则称A为α-双对角占优矩阵。首先推广α-双对角占优矩阵的概念到广义α-双对角占优,然后得到了判别广义α-双对角占优矩阵的一个充分必要条件,改进和推广了已有的结论,进一步丰富和完善了α-双对角占优矩阵的理论。

Let A=（aij）∈C^n×n, if there existsa∈（O,1）, which can make {aiiajj}≥（RiRj）^a（SiSj）^1-a be right for i≠j（i,j∈N={1,2,…,n}） 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.