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ju you fei ling yuan su lian de dui jiao zhan you ju zhen wei fei qi yi de ding li de yi ge jian duan zheng ming
Author(s): 
Pages: 75-77
Year: Issue:  1
Journal: Acta Scientiarum Naturalium Universitatis Neimongol

Keyword:  严格对角占优矩阵非零元素链非奇异不可约可约矩阵简短证明排列矩阵定理证明充分条件性质;
Abstract: <正> 设 A=(aij)是 n 阶对角占优矩阵,即若记 N={1,2,…,n},则对任意 i∈N 都有|an|≥sum from j=1 j≠i to n |aij|.本文所涉及的矩阵总假定是对角占优的。记 J(A)={i∈N||aii|>sum from j=1 j≠i to n |aij|}.当 J(A)=N 时,A 为严格对角占优矩阵,当 J(A)≠Φ,且 A 不可约时,A 是不可约对角占优矩阵,这两种矩阵都是非奇异的。当 J(A)≠Φ,A 为可约矩阵时,一九七四年 P.N.shivakumar 和 kim Ho Chew 给出了它为非奇异的一个充分条件:定理.设 A 为可约矩阵,J(A)≠Φ,若对每个 (?)J(A),都存在由 A 中非零元素构成的序列(也叫非零元素链):aii1,ai1i2,…,ais-1is,is∈J(A),那末 A 是非奇异的.P.N Shivakumar 和 kim Ho Chew 在证明此定理时,引用了 M—矩阵的性质,篇幅
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