Complex singular Wishart matrices and applications∗
نویسندگان
چکیده
In this paper, complex singular Wishart matrices and their applications are investigated. In particular, a volume element on the space of positive semidefinite m×m complex matrices of rank n < m is introduced and some transformation properties are established. The Jacobian for the change of variables in the singular value decomposition of general m × n complex matrices is derived. Then the density functions are formulated for all rank n complex singular Wishart distributions. From this, the joint eigenvalue density of low rank complex Wishart matrices are derived. Finally, application of these densities in information theory is given.
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