2 problems

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…