7 problems

Let $A=A_s+A_d\varepsilon$ be an $n\times n$ dual number matrix and let $k\in\mathbb{N}$. Here $O$ denotes the zero matrix, and $\rho(A_s)$ denotes the spectral radius of the stand…

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…

Let $A$ be an $n$-by-$n$ doubly nonnegative matrix, and let the conventional critical exponent be the least real number $m$ such that $A^\alpha$ is doubly nonnegative for every suc…

Persistence conjecture. Some of the statements (ii)–(vii) of Theorem should still hold under the weaker assumption that $A$ is irreducible and power nonnegative.

Critical exponent conjecture. For all integers $n\geq 2$,

Let $A$ be a max-algebra matrix with CSR data indexed by $k$, where $\boldsymbol{\lambda_k}$ are the corresponding eigenvalues, $C_k$ and $R_k$ are the associated column and row ma…

Conventional critical exponent conjecture. The conventional critical exponent for $n$-by-$n$ doubly nonnegative matrices is always $n-2$.