6 problems

A $\tau$-matrix is a matrix in the relevant class of matrices considered in the source, and a GKK matrix is a matrix satisfying positivity of principal minors, weak sign-symmetry,…

A GKK matrix is a matrix satisfying positivity of principal minors, weak sign-symmetry, and eigenvalue monotonicity. A matrix is stable if its spectrum lies entirely in the open ri…

Let $A\in\mathbb{R}^{m\times n}$ be a real nonsquare matrix. Let $\mathcal{M}$ be the index set consisting of $k$-tuples of integers in the range $1,\ldots,m$. For…

Let $\Gamma(t)$ be the matrix defined in the paper's Lemma. Asymptotic positive-stability conjecture. There exists $t_1>0$ such that, for every $t>t_1$, the matrix $\Gamma(t)$ is s…

Let $H\foral R^{n\times n}$ be symmetric and entrywise nonnegative, with geometrically simple spectral-radius eigenvalue $\rho(H)$. Let $v,w\in\mathbb R^n$ satisfy $v>0$ and $w>0$.…

Let $A$ be a singular symmetric M-matrix whose eigenvalue $0$ is geometrically simple, and let $v w^T$ be a positive rank-one perturbation. Symmetric singular M-matrix conjecture.…