| 外微分在雅可比行列式计算中的应用 |
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| 引用本文： | 石爱菊,夏洁. 外微分在雅可比行列式计算中的应用[J]. 安徽大学学报(自然科学版), 2007, 31(3): 9-11. DOI: 10.3969/j.issn.1000-2162.2007.03.003 |
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| 作者姓名： | 石爱菊 夏洁 |
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| 作者单位： | 南京邮电大学,数理学院,江苏,南京,210003;解放军电子工程学院,训练部,安徽,合肥,230037 |
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| 摘 要： | 通常计算Jacobi行列式的方法是通过先求出行列式的每个元素再求得行列式的值.利用相同元素的外微分为零的性质来求解Jacobi行列式,这种方法的最大优点是避开了求解变换的行列式的元素,所以比通常的方法要简便得多.作为这一方法的应用,我们计算了几个重要的Jacobi行列式,推导了矩阵F分布的顺序特征值的联合分布.
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| 关 键 词： | 外积 Jacobi行列式 外微分形式 变换 矩阵F分布 |
| 文章编号： | 1000-2162（2007）03-0009-03 |
| 修稿时间： | 2006-10-16 |
Application of the exterior differential forms in calculating the Jacobins |
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| SHI Ai-ju,XIA Jie. Application of the exterior differential forms in calculating the Jacobins[J]. Journal of Anhui University(Natural Sciences), 2007, 31(3): 9-11. DOI: 10.3969/j.issn.1000-2162.2007.03.003 |
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| Authors: | SHI Ai-ju XIA Jie |
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| Affiliation: | 1. College of Mathematics and Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003,China; 2. Training Department, Electronic Engineering Institnte of PLA, Hefei 230037, China |
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| Abstract: | Usually we calculates Jacobi through calculate the Jacobi matrix's elements.This paper uses property that the same elements have zero exterior product to calculate the Jacobi.The greatest merit of our method is it need not to calculate the elements about the Jacobi matrix.So it is much simpler than the former one.To make use of our method,this paper proves some important Jacobi interested to us through this method.And deduces the eigenvalue' joint distribution of matrix F distribution. |
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| Keywords: | exterior product Jacobin exterior differential forms transformation matrix F distribution |
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