2 problems

Let $X_\sharp\in\mathbb{R}^{d\times r}$ be a rank-$r$ matrix, let $\mathcal{X}$ denote the feasible region, and set … Here $\operatorname{dist}_{\|\cdot\|_{2,1}}$ denotes distance…

Let $\operatorname{LS}_n(r,s)$ denote the set of matrices that can be written as the sum of an $n\times n$ matrix of rank at most $r$ and an $n\times n$ matrix with at most $s$ non…