I've stumbled across some math I've never really encountered before, and I would love it if someone could provide me with some useful references and texts on it. I'm dealing with integration over the space of matrices, as in Random Matrix Theory and such. Specifically, I think I've narrowed my confusion down to two different types of matrix integration, some of the form \begin{equation}G=\int dA \,f(A)\end{equation} Where $A$ is a matrix of some sort, and $f(A)$ is also a matrix. Then there are integrals of the form \begin{equation}H=\int dA \,f(|A|)\end{equation} Where $|A|$ is the determinant. This also includes integrals involving $\mathrm{tr}(A)$, i.e., integrals of scalar functions of matrices. Essentially, integrals of matrix functions of matrices, and integrals of scalar functions of matrices over some measure of matrices.
Also, is there any good literature on extensions of contour integration and complex analysis to these sorts of matrix functions?
Sorry for the long question.
