6 problems

Newton's inequalities. For every M-matrix, inverse M-matrix, or matrix similar to one of these, the normalized characteristic-polynomial coefficients satisfy

Berman–Rantzer conjecture. There is a positive $t_1$ such that, for every $t>t_1$, all eigenvalues of $B(t)$ lie in the open right half plane.

Let $T$ be the matrix considered in the approximation problem, with positive elements and diagonal dominance as in the preceding discussion. Inverse $M$-matrix conjecture. We conje…

Elementwise error-rate conjecture. For general $\mathcal{E}^*$, the rates of convergence of the elementwise $\ell_{\infty}$ error are at least comparable to those achieved by…

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.…

Let $K$ be a regular singular $M$-matrix and let $u_1,u_2,v_1,v_2$ be the vectors associated with $K$ as in the source. The scalar products $u_1^Tv_1$ and $u_2^Tv_2$ compare the co…