5 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…

Stubborn-matrix conjecture. With probability $1-o(1)$, $M_n$ is stubborn.

Rank-resilience conjecture. With probability $1-o(1)$,

Random regular graph singularity conjecture. For every $3\leq d\leq n-1$, $A_{n,d}$ is nonsingular with probability $1-o(1)$.