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You got a vector $x \neq 0$ with $x \in \mathbb{R}^3$. I have to show that there is a bijection between the stabilizer $\{A \in O_3(\mathbb{R}) \mid Ax = x \}$ and $O_2(\mathbb{R})$. Can someone tell me what the stabilizer looks like and how he is related with the $O_2$ group ? (The group action is the standard matrixproduct as you see)

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    thanks. This helps a lot :)2012-09-30

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