4 problems

Let $M$ be a $\{-1,1\}$ matrix. Call $M$ good if every matrix obtained by independently switching any subset of its diagonal entries is nonsingular. Let $M_n$ be a random…

For a $\{-1,1\}$ matrix $M$, let $\operatorname{Res}(M)$ be the minimum number of entries that must be switched from $1$ to $-1$ or vice versa in order to make $M$ singular. Let…

Let $M\in\{\pm1\}^{n\times m}$ with $m\geq n$, and let $\operatorname{Res}(M)$ be the least number of entry-flips needed to produce from $M$ a matrix whose rank is strictly less th…

Global resilience conjecture. Then $G$ has global resilience $(1/4+o(1))nd$ with respect to being $C_k$-free.