Suppose I am given a pdf of a Inverse Wishart distribution as follows.
$$P = \frac{|\Phi|^{(v/2)}}{(2\pi)^{(vp/2)} \Gamma_p(v/2)} |\Sigma|^{-((v+p+1)/2)} \exp\left\{-\frac{1}{2} \operatorname{tr}(\Phi \Sigma^{-1})\right\}$$
How can I integrate over $\Sigma$? That is I want to get $\int_\Sigma P \, d\Sigma$
I don't know how to integrate over a matrix. Can someone help please, or give some references, please?
As per the wiki link and the description in the Conjugate distribution section in the page, I should be getting an answer similar to the marginalized $P(X\mid\Phi, v)$ equation right?