4 problems

Let $\mathcal{H}_n$ be the set of $n\times n$ positive semidefinite Hermitian matrices. For $A=[a_{i,j}]\in\mathcal{H}_n$, let $A(i,j)$ be obtained by deleting row $i$ and column…

Bapat–Sunder's conjecture. The largest eigenvalue of $F_A$ should satisfy

Let $\mathcal{H}_n$ be the set of $n\times n$ positive semidefinite Hermitian matrices. For matrices $A=[a_{i,j}]$ and $B=[b_{i,j}]$ in $\mathcal{H}_n$, define the Hadamard product…

Let $f_{312}(n)$ be the maximum permanent of an $n\times n$ 0-1 matrix avoiding the permutation pattern 312. Let $\mathcal{M}_n(\ast,\circ)$ be the set of $n\times n$ matrices obta…