you see how the sampling distribution of the covariance matrix follows a wishart distribution (for the multivariate normal case)?

does it make sense to say then that the sampling distribution of the

*correlation*matrix also follows a wishart distribution? it makes sense to me because i look at correlation matrices as scaled covariance matrices, but i need this piece of info for a little "debate" i'm having with my advisor and i cant find any sources who specifically talk about the correlation matrix.

just wanna verify this with someone who's a little bit more well-versed in these topics... a reference (book, journal article, etc...) would be great! thanks!