I wonder, is it possible for two matrices in $\mathrm{SO}(n), \ n>2$ with rational entries to generate a free subgroup of $\mathrm{SO}(n)$? If yes, is it possible to construct two such matrices ? For irrational coefficients there is no problem of course.
2026-03-30 08:31:14.1774859474
Orthogonal matrices with rational coefficients generating free subgroup
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