# Can Wishart be close to Normal distribution?

I'm trying to figure out if Wishart can be close to Normal for a number of degrees of freedom enough large.

By the central limit theorem, because the chi-squared distribution is the sum of k

The Wishart distribution (when dimension is 2 or higher) is a distribution on a space of matrices, if the underlying space had dimension $d$, the space of symmetric positive matrices $d \times d$ has dimension $d(d+1)/2$, so for approximating Wishart by a normal you would need a normal of that dimension which in addition fulfills the (non-linear) conditions necessary to be a positive definite matrix. That doesn't sound like being possible, so I believe the answer to your question is NO.