 A different type of generalization is the normal-inverse-Wishart distribution, essentially the product of a multivariate normal distribution with an inverse Wishart distribution.When the scale matrix is an identity matrix, formula_96 is an arbitrary orthogonal matrix, replacement of formula_97 by formula_98 does not change the pdf of formula_99 so formula_64 belongs to the family of spherically invariant random processes (SIRPs) in some sense.Thus, an arbitrary "p-vector" formula_101 with formula_102 can be rotated into the vector formula_103 without changing the pdf of formula_104, moreover formula_105 can be a permutation matrix which exchanges diagonal elements.