# Proving a property of the Wishart distribution

I would like to prove that, if $X \sim W(V,n)$, then $CXC^T \sim W(CVC^T,n)$ where $W$ is a Wishart distribution. A point in the right direction would be welcome - happy to admit that I may have missed something obvious here.

• Have you thought of using the representation of a Wishart matrix $X \sim \mathfrak{W}(V,n)$ as a sum of $n$ matrices $Y_iY_i^\text{T}$ when the $Y_i$ are iid $\mathfrak{N}(0,V)$? – Xi'an Feb 4 '16 at 12:27
• Ah I see - so it comes down to $E[ C Y_i Y_i^T C^T] = C E[Y_i Y_i^T] C^T = CVC^T$. So yes, I had missed something obvious :) – Pete Feb 6 '16 at 18:47