| 摘要: |
| 用Zn表示所有n阶符号模式矩阵,这些矩阵非主对角线项都是非正.对于一个符号模式矩阵A∈Zn和任意两个实矩阵,如果sgn(B1B2)∈Zn,那么称这一特性为Zn内的闭特征.如果符号模式矩阵A∈Zn(n≥3)具有Zn内的闭特征,那么A必定可约.最后给出了这类符号模式矩阵的结构刻画. |
| 关键词: 符号模式矩阵 闭特征 可约 |
| DOI： |
| 分类号: |
| 基金项目: |
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| On the Zn sign pattern matrices |
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FANG Maozhong1, ZHANG Jizhou2
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1.School of Mathematics and Information,Shanghai Lixin University of Commerce;2.College of Mathematics and Sciences,Shanghai Normal University
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| Abstract: |
| Let Zn dente the set of all square sign pattern matrices of order n whose off-diagonal entries are non-positive.For a sign pattern matrix A∈Zn and two arbitrary real matrices B1,B2 with sign pattern A,if sgn(B1B2)∈Zn,then we call this property the closure property of Zn.We prove that if A∈Zn(n≥3) and A has the closure property of Zn,then A must be reducible.We also characterize this kind of Zn sign pattern matrices. |
| Key words: sign pattern matrix closure reducible |
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