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:

R(theta) = begin{bmatrix} cos theta & - sin theta \ sin theta & cos theta end{bmatrix}

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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