You know what’s surprising?
Rotations are linear transformations.
I guess lo conocí but no entendí. Like, I could write you the matrix formula for a rotation by θ degrees:
But why is that linear? Lines are straight and circles bend. When you rotate something you are moving it along a circle. So how can that be linear?
I guess 2-D linear mappings ℝ²→ℝ² surprise our natural 1-D way of thinking about “straightness”.
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