3 problems

Let $A$ and $B$ be matrices, let $\sigma_{(\max+)}(A)$ and $\sigma_{(\max+)}(B)$ denote their max-plus eigenspaces, and let $\mathscr{P}_{\infty}(A)$ and $\mathscr{P}_{\infty}(B)$ de…

Critical-eigenvector conjecture. If, for every other $w=(0,w_1,w_2)\in\sigma_{\max+}(A)$, there exists an $\alpha>0$ with $\alpha\in\mathbb{R}$ such that $v_1=w_1+\alpha$ and…

Let $CE_n$ denote the critical exponent for $n$-by-$n$ generalized doubly nonnegative matrices, and let $MIP_n$ be the maximum index of primitivity among primitive $n$-by-$n$ gener…