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Existence of Rational Orthogonal Matrices

Question: Let $A\in\mathbb{R}^{n \times n}$ be an orthogonal matrix and let $\varepsilon>0$. Then does there exist a rational orthogonal matrix $B\in\mathbb{R}^{n \times n}$ such that $\|A-B\|<\vareps …
Peter J.C. Dickinson's user avatar