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Thread: prove that distinct reflections commute iff...

  1. #1
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    prove that distinct reflections commute iff...

    let $\displaystyle m$ and $\displaystyle l$ be lines in $\displaystyle E_2$, and the reflection of $\displaystyle l$ is the mapping $\displaystyle \Omega_l$ of $\displaystyle E_2$ to $\displaystyle E_2$ defined by $\displaystyle \Omega_lX = X - 2N((X - P) \cdot N)$ where $\displaystyle N$ is the unit normal to $\displaystyle l$ and $\displaystyle P$ is any point on $\displaystyle l$

    Show that two distinct reflections $\displaystyle \Omega_l$ and $\displaystyle \Omega_m$commute if and only if $\displaystyle m \perp l$.
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  2. #2
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    I solved it, so never mind. This can be deleted, if a moderator would be willing.
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