| 矩阵乘积数值特征的不变性及在统计中的应用 |
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| 引用本文： | 张宝学,张丹松. 矩阵乘积数值特征的不变性及在统计中的应用[J]. 北京理工大学学报(英文版), 2001, 10(2): 125-130 |
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| 作者姓名： | 张宝学 张丹松 |
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| 作者单位： | 1. 北京理工大学应用数学系,
2. 五邑大学经济管理系, |
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| 摘 要： | 利用矩阵论和线性模型理论研究矩阵乘积数值特征的不变性及在统计中的应用 ,给出了乘积AB- C的数值特征和关于每个最小模g逆不变的充分必要条件 .并将这些结果应用到研究一般高斯马尔可夫模型下均值的最佳线性无偏估计 ,以及加权最小二乘估计和最小二乘估计之间相等的关系上 .
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| 关 键 词： | g逆 列空间 零空间 秩 迹 不变性 |
| 收稿时间： | 2000-09-21 |
Invariance of Numerical Character of Matrix Products and Their Statistical Applications |
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| ZHANG Bao xue and ZHANG Dan song. Invariance of Numerical Character of Matrix Products and Their Statistical Applications[J]. Journal of Beijing Institute of Technology, 2001, 10(2): 125-130 |
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| Authors: | ZHANG Bao xue and ZHANG Dan song |
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| Affiliation: | Dept. of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, China;Dept.of Economics Management, Wuyi University, Jiangmen, Guangdong 529020, China |
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| Abstract: | To study the invariance of numerical character of matrix products and their statistical applications by matrix theory and linear model theory. Necessary and sufficient conditions are established for the product AB -C to have its numerical characters invariant with respect to every minimum norm g inverse, respectively. The algebraic results derived are then applied to investigate relationships among BLUE, WLSE and OLSE under the general Gauss? Markoff model. |
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| Keywords: | g inverse range space null space rank trace invariance |
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