3 problems

Rank-$r$ projection sparsification conjecture. There exists a constant $C_r$ such that one can choose indices $i_1,\dots,i_N\in[m]$ with

Let $A_1,\dots,A_n\in\mathcal{M}_d$ be positive semidefinite, and suppose that nonnegative coefficients $\lambda_1,\dots,\lambda_n$ summing to one satisfy … For…

Let $\Phi$ be a compressed sensing matrix with $n$ rows, $N$ columns, and sparsity parameter $k$. Let $\alpha$ satisfy $N<n^{\alpha}$, and let the density of $\Phi$ denote the prop…