I am considering real $n$-by-$m$ matrices of the following type:

$$ M=SM^\prime,\\ M^\prime_{ij}\sim^{iid}N(0,1). $$

Here, $S$ is a fixed $n$-by-$n$ matrix and the entries of $M^\prime$ (same size as $M$) are just i.i.d Gaussian. It is important that the considered matrices are rectangular and not simply square. $S$ can be identity but, ideally, should be an arbitrary full-rank matrix.

As far as I know, in the special case of $S=I, n=m$ this construction is called the real Ginibre ensemble. Can anyone suggest some literature/references for the more general case? I'm particularly interested in spectral properties of these matrices such as singular value/vector distributions.