Journal of East China Normal University(Natural Sc ›› 2010, Vol. 2010 ›› Issue (1): 85-90.

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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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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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