5 problems

Let $(\mathcal{G},\ast,0,\leq)$ be an ordered Abelian group, let $\mathcal{S}=\mathcal{G}^{(0)}\cup\mathcal{G}^{(1)}\cup\{\varepsilon\}$ be the associated supertropical semifield,…

Let $B$ be a non-triangular definite matrix in $T^\ell T^u$, where $T^\ell$ and $T^u$ are the lower- and upper-triangular submonoids generated by elementary matrices, and let…

Let $A$ be a nonsingular matrix, and let $A^\nabla$ denote its quasi-inverse matrix. Suppose that $A^\nabla$ has $n$ distinct eigenvalues. Quasi-inverse eigenvector conjecture. The…

Let $A$ be a nonsingular matrix with $n$ distinct eigenvalues. Suppose that the eigenvectors of $A$ are dependent, and let $A^\nabla$ denote its quasi-inverse matrix. Write…

Characteristic-polynomial reversal conjecture. One has