4 problems

Let $A$ be a square matrix over a subring $\mathcal R$ of $\mathbb R$. Its nonzero spectrum is the multiset of its nonzero eigenvalues. Boyle–Handelman's strong generalized spectra…

Let $V(n)$ be the Gessel-Viennot matrix associated with the graph $G(n)$, and let the paper's transit-free resolution identify the associated graph with the Aztec diamond graph. Th…

Let $A$ and $B$ be $n\times n$ skew-symmetric real matrices. Two such matrices have equal corresponding principal minors of all orders if, for every subset $X\subseteq [n]$, the pr…

Let $A$ and $B$ be positive rational matrices. They are shift equivalent over $\mathbb Q_+$ when they are shift equivalent using matrices with entries in $\mathbb Q_+$, and strongl…