华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (1): 85-90.

• 应用数学与基础数学 • 上一篇    下一篇

四元数矩阵的奇异 Beta 分布和 F 分布

李斐1, 薛以锋2   

  1. 1. 烟台大学数学系, 山东 烟台 264005; 2.华东师范大学数学系, 上海 200241
  • 收稿日期:2009-03-15 修回日期:2009-04-29 出版日期:2010-01-25 发布日期:2010-01-25
  • 通讯作者: 薛以锋

Generalized Beta and F distributions of quaternion matrix argument (Chinese)

LI Fei1,XUE Yi-feng2   

  1. 1. Department of Mathematics,Yantai University, YantaiShangdong 264005, China; 2. Department of Mathematics,East China Normal University, Shanghai200241,China
  • Received:2009-03-15 Revised:2009-04-29 Online:2010-01-25 Published:2010-01-25
  • Contact: XUE Yi-feng

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摘要： 应用四元数矩阵的奇异 Wishart 分布的密度函数表达式和奇异四元数矩阵奇异值分解的工具, 求得了奇异四元数矩阵变换 textbfemphX=textbfemphBYB^mathrm T 的 Jacobi 行列式. 利用奇异四元数矩阵的广义逆定义了四元数矩阵的奇异 Beta 分布和 F 分布, 结合奇异四元数矩阵数乘变换的 Jacobi 行列式,给出了四元数矩阵的奇异 Beta 分布和 F 分布的密度函数表达式. 最后, 给出了满足两种分布的奇异四元数矩阵的非零特征值的联合密度函数.

关键词: 奇异四元数矩阵, Beta 分布, 特征值联合密度函数, 奇异四元数矩阵, Beta 分布, 特征值联合密度函数

Abstract:

This paper computed the Jacobian of transformation textbfemphX=textbfemphBYB^mathrm T of singular quaternion matrices by using of the singular value decomposition of quaternion matrix and the density function of singular quaternion Wishart matrix. Then we defined the Beta and F distributions of quaternion matrix argument,and gave the density functions of the Beta and F distribution and the joint density functions of the nonzero eigenvalues of the singular quaternion matrices which satisfy the Beta or F distribution.

Key words: Beta distribution, joint density function of eigenvalues, singular quaternion matrix, Beta distribution, joint density function of eigenvalues

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