  In this paper, we want to show the Restricted Wishart distribution is
equivalent to the LKJ distribution, which is one way to specify a uniform
distribution from the space of positive definite correlation matrices. Based on
this theorem, we propose a new method to generate random correlation matrices
from the LKJ distribution. This new method is faster than the original onion
method for generating random matrices, especially in the low dimension
($T<120$) situation.
