3 problems

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

Let $a_n$ be the number of acyclic directed graphs with $n$ labeled vertices, and let $b_n$ be the number of real $n\times n$ matrices with entries in $\{0,1\}$ whose eigenvalues a…

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…