【摘要】 <正>1引言及记号因为非奇异H-矩阵主对角元非零,所以本文总假定所涉及矩阵主对角元非零,并且设A=(aij)∈Cn×n为n阶复方阵,N={1,2,…,n}．记N1={i∈N |Pi(A)<|aii|<Ri(A)), N2={i∈N |Ri(A)<|aii|<Pi(A)}, N3={i∈N | |aii|≥Ri(A)>Pi(A)}, N4={i∈N | |aii|≥Pi(A)>Ri(A)}, N5={i∈N | |aii|>Pi(A)=Ri(A)},N0={i∈N | |aii|≤Ri(A),|aii|≤Pi(A)},即N=N1∪N2∪N3∪N4∪N5∪N0．更多还原

【Abstract】 In this paper,an equivalent condition is given for the strictlyα- diagonally dominant matrices firstly. By this theorem,we can obtain some new practical criteria for nonsingular H-matrix.At the same time,a range of eigenvalues is given for a kind of nonsingular H-matrix.In the end,two examples are given.One shows some nonsingular H-matricx that can not be proved by [1,Theorem 2] but can be proved by the criterion in this paper,the other shows that the results of [4] are improved.更多还原