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Results tagged with orthogonal-groups
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user 13972
41
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Is $O_n({\bf Q})$ dense in $O_n({\bf R})$?
There's an easy argument based on the Cayley transform: If $a$ is a skew-symmetric $n$-by-$n$ real matrix, then $I_n+a$ is invertible (since $(I_n-a)(I_n+a)=I_n-a^2$ is a positive definite symmetric …
- 108k
38
votes
Is SO(4) a subgroup of SU(3)?
Maybe the simplest argument, if you know something about compact Lie groups, is that SO(4) and SU(3) both have rank 2, i.e., they each contain a maximal torus, which is $S^1\times S^1$. Since all max …
- 108k