2 problems

Von Neumann–Goldstine conjecture. The typical value of $s_{\min}(G)$ is of order $n^{-1/2}$, while the condition number $\kappa(G)$ is of order $n$.

Let $p$ and $q$ satisfy $p\le 2\le q$, and let $A=(a_{ij})_{i\le m,j\le n}$ be a deterministic $m\times n$ matrix. Write $p^*$ for the Hölder conjugate of $p$, and let…