Given matrix $M\in\Bbb R_{\geq0,\leq b}^{n\times n}$, is there a nice method to characterize matrices $Q\in\Bbb R_{\geq0,\leq b}^{n\times n}$ such that $$\mathsf{rank}(M-Q)= \mathsf{rank}(Q),\quad M-Q\in\Bbb R_{\geq0,\leq b}^{n\times n}?$$