2 problems

Let $I_k$ be the $k\times k$ identity matrix. For an $n\times n$ matrix, let $\mathrm{M}(n,I_k)$ denote the maximum possible number of $1$-entries in a strongly $I_k$-forcing matri…

Spectral arbitrariness conjecture. The patterns $\mathcal{T}_n$ are spectrally arbitrary for all $n\geq 2$, and hence are potentially nilpotent.