Abstract: The concepts of local (α,β)-diagonally dominant matrix were introduced. Under the condition of local (α,β)-diagonally dominant matrix with a nonzero elements chain, by constructing a positive diagonal matrix [WTHX]X[WTBZ], the conclusion that [WTHX]B=AX[WTBZ] was α-diagonally dominant matrix with a nonzero elements chain was presented, and a criterion for nonsingular [WTHX]H[WTBZ]-matrix was obtained. The outcome implies that the extended local (α,β)-diagonally dominant concept is a development for matrix's diagonally dominance's theory, and a strong tool for researching [WTHX]H[WTBZ]-matrix and [WTHX]M[WTBZ]-matrix.

Key words: Nonsingular matrix, Nonzero elements chain, Local (α,β)-doubly diagonally dominance

摘要： 给出了局部(α,β)-对角占优矩阵的相关概念。对于复矩阵[WTHX]A[WTBX] ，在具非零元素链的局部(α,β)-对角占优矩阵的条件下，通过建立正对角阵[WTHX]X[WTBX] ,转化为具非零元素链的α-对角占优矩阵，从而获得了[WTHX]A[WTBX] 为非奇[WTHX]H[WTBX]-矩阵的判别准则。结果表明，提出这种延伸的局部(α,β)-对角占优矩阵的概念，是对矩阵的对角占优理论的完善，是研究[WTHX]H[WTBX]-矩阵、[WTHX]M[WTBX]-矩阵的有力工具。

关键词: 非奇矩阵, 非零元素链, 局部(&alpha, &beta, )-对角占优