| 极端U_1矩阵的结构与计数 |
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| 引用本文： | 杨尚俊,徐常青. 极端U_1矩阵的结构与计数[J]. 安徽大学学报(自然科学版), 2012, 36(3): 1-7 |
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| 作者姓名： | 杨尚俊 徐常青 |
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| 作者单位： | 1. 安徽大学数学科学学院,安徽合肥,230039
2. 浙江农林大学数学系,浙江杭州,311300 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 相关文献在研究单纯形上的双随机算子和极端双随机算子的充要条件时,成功地利用U1矩阵和极端U1矩阵的工具,取得丰硕成果.其在给出U1矩阵是极端U1矩阵的必要条件基础上,进一步给出U1矩阵是极端U1矩阵的充要条件及对称非负矩阵是极端U1矩阵的充要条件.论文继续深入研究极端U1矩阵的性质,包括其直和结构、置换相似类个数的计算和谱半径估计,并对相关文献提出的猜想给出肯定性的证明.
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| 关 键 词： | 不可约矩阵 谱半径 极端U矩阵 矩阵的直和 正交矩阵 |
Construction and counting of extreme U1 matrices |
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| YANG Shang-jun , XU Chang-qing. Construction and counting of extreme U1 matrices[J]. Journal of Anhui University(Natural Sciences), 2012, 36(3): 1-7 |
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| Authors: | YANG Shang-jun XU Chang-qing |
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| Affiliation: | 1.School of Mathematical Sciences,Anhui University,Hefei 230039,China; 2.Department of Mathematics,Zhejiang A and F University,Hangzhou 311300,China) |
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| Abstract: | Some reference uses U1 and extreme U1 matrices to investigate the necessary and sufficient condition for a quadratic operator defined on the simplex to be a quadratic stochastic operator or an extreme quadratic stochastic operator.Other reference presented a necessary and sufficient condition for a U1 matrix to be an extreme U1 matrix(other reference only presented the necessary condition),and a necessary and sufficient condition for a symmetric nonnegative matrix was an extreme U1 matrix.In this paper,we continued to investigate extreme U1 matrices including the structure of an extreme U1 matrix,counted the number of n×n extreme U1 matrices and computed the spectral radius of an n×n extreme U1 matrix.Finally we proved the conjecture given in other articles. |
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| Keywords: | irreducible matrices the spectral radius extreme U1 matrices direct sum of matrices orthogonal matrices |
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