Plane Reflection is Space Rotation
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Theorem
Let $M$ be a straight line in the plane passing through the origin.
Let $s_M$ be the reflection of $\R^2$ in $M$.
Then $s_M$ is the rotation of the plane in space through one half turn about $M$ as an axis.
Proof
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Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 28$. Linear Transformations: Example $28.4$