4 problems

Let $A$ be a minimally AP-irreducible sign pattern matrix of order $n$ whose diagonal entries are all zero. A sign pattern matrix $A$ is minimally AP-irreducible if it is AP-irredu…

Let $B$, $C$, and $E$ be real matrices satisfying … The zero entries of $E$ are contained in a submatrix with either 2 rows or 2 columns. Rational realization conjecture. There exi…

Li et al.'s conjecture. If $r\geqslant t-2$, then the minimum rank of $S$ over the rationals is also $r$.

Let $\mathcal{T}_n$ be the set of $n\times n$ tridiagonal real matrices whose sub-diagonal entries are negative, super-diagonal entries are positive, the $(1,1)$ entry is negative,…