I try to evaluate the pdf of a multivariate t-distribution in Matlab. Unfortunately the function is only defined for a correlation matrix and not for a covariance matrix. I guess i can rescale the input data and use the Matlab function.
In 1d this is done by dividing the data through the standard deviation $\sigma$, computing the pdf, and dividing the result by $\sigma$.
How is this done in the multivariate case?
An example:
I create random draws where $X \sim \mathcal{N}(0,{\Sigma})$ and $\Sigma$ may equal any covariance matrix. In the next step I want to evaluate the pdf of a t-distribution of my data $X$ with some degree of freedom $\nu$. I want to know $p(X|\Sigma,\nu)$.
In Matlab the function mvtpdf accepts only correlation matrices. In my understanding I have to scale my data $X$ with some transformation $T(\cdot)$ to match the different scales. How do I find $T(\cdot)$?