6 problems

Let $S \subseteq \mathbb{Q}^{n \times n}$ be a finite semigroup of rational matrices containing the zero matrix, generated by a set $S_0$. The mortality threshold of $S$ is the min…

The paper considers rational matrices $G(\lambda)$ and strong linearizations $\mathcal{L}(\lambda)$, with the preceding result providing a method to obtain strong linearizations fo…

Rational-matrix finiteness conjecture. Every finite family of rational matrices has the finiteness property. The source says this has only been conjectured and gives no resolution.

Blondel–Jungers conjecture. Every finite set of matrices with rational entries has the finiteness property.

The symmetric rational orthogonal zero-pattern conjecture. For any hermitian $X\in U(n)$ there exists a symmetric $Z\in O_n(\mathbb{Q})$ such that $\underline{X}=\underline{Z}$ and

Let $X$ be an $m\times n$ matrix over a field. Its zero-pattern (or support) is the $(0,1)$-matrix $\underline{X}$ defined by … Let $O(n)$ denote the real orthogonal $n\times n$ ma…