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