Abstract: Let [WTHX]A[WTBZ]=([WTBX]aij)∈Cn×n, if there exists α∈(0,1) which can make |aii|≥Rαi(A)S1-αi(A)  be right for i∈N={1,2,…,n}, then [WTHX]A[WTBZ] is called an Ostrowski diagonally dominant matrix. We extended the concept to generalized Ostrowski diagonally dominant matrix，and obtained a new criteria conditions for a matrix to be a nonsingular [WTHX]H[WTBZ]-matrix. The theory of Ostrowski diagonally dominant matrix and nonsingular [WTHX]H[WTBZ]-matrix was improved and completed. These conclusions provide strong basis for the research of relative fields, such as computational mathematics, matrix theory, control theory, mathematical economics, etc.

Key words: Nonsingular [WTHX]H[WTBZ]-matrix , Strictly Ostrowski diagonally dominant matrix , Generalized strictly Ostrowski diagonally dominant matrix

摘要： 设A=(aij)∈Cn×n ,若存在α∈(0,1),使∀i∈N ={1,2,…,n},|aii|≥Rα
i (A )S1-α
i (A ),则称A 为
Ostrowski对角占优矩阵。首先推广Ostrowski对角占优矩阵的概念到广义Ostrowski对角占优矩阵;最后得到了
判别非奇异H -矩阵的一个判定方法。进一步丰富和完善了Ostrowski对角占优矩阵和非奇异H -矩阵的理论,为
计算数学、矩阵论、控制论、经济数学等相关领域的研究奠定了坚实的基础。

关键词: 非奇异H -矩阵 , 严格Ostrowski对角占优矩阵 , 广义严格Ostrowski对角占优矩阵