Consider a random rectangular matrix $X\in\mathbb{R}^{N\times P}$ where each entry is drawn from iid distribution with mean $m$ and variance $s^2$, and denote $X^+$ the Moore-Penrose pseudo-inverse.
What is the distribution of the eigenvalues $\rho(\lambda_{A X^+})$ of:
$$A X^+ = A (X'X)^{-1} X'$$
for a constant $A\in\mathbb{R}^{N\times P}$, where $N,P \to \infty$ with constant ratio $\alpha=P/N$?
