Abstract: Let [WTHX]A[WTBX]=(aij)∈Cn×n, [WTBZ]if there exists[WTBX] α[WTBZ]∈（0，1）, which can make[WTBX] |aiiajj|≥（RiRj）α（SiSj）1-α[WTBZ] be right for[WTBX] i≠j（i，j∈N={1，2，…，n}）, [WTBZ]then [WTHX]A[WTBZ] 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 [WTHX]A[WTBZ] 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.

Key words: Irreducible matrix, α-Doubly diagonally dominant, Generalized α-doubly diagonally dominant matrix

摘要： 设=(aij)∈Cn×n ，若存在α∈（0，1），使i≠j（i，j∈N={1，2，…，n}）有|aiiajj|≥（R iRj）α（SiSj）1-α，则称[WTHX]A[WTBX]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。

关键词: 不可约矩阵, &alpha, -双对角占优矩阵, 广义严格&alpha, -双对角占优矩阵