3 problems

Let $J$ be an entrywise positive, diagonally balanced symmetric real $n\times n$ matrix, where $n\geq 2$. Diagonal balance means that, for every $i=1,\ldots,n$,…

Let $J$ be a positive, diagonally balanced symmetric matrix, and let $S$ denote the comparison matrix used in the determinant bound. Largest-entry-free determinant conjecture. One…

Let $n \geq 3$ and let $S(\alpha,m)=\alpha I_n+m\mathbf{1}_n\mathbf{1}_n^\top$. A symmetric diagonally dominant matrix $J$ is assumed to satisfy $0<J\leq S(\alpha,m)$. Inverse infi…