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Does this mean that to apply a rotation that is equal and opposite of R, you can instead multiply by R^T? Or am I too tired to be thinking about linear algebra right now


To dshernan, this means that R^T will rotate as opposite to R.


What's the geometric meaning of rotating by R^T


I don't really understand how this works. Does it work just because of the change of basis method? Matrix multiplication? Inverses?


Does the orthonormal basis preserve the magnitudes of the standard basis/would the graphic look different if the magnitudes of (e1,e2,e3) were larger/smaller?


This may not be related, but we often see that instead of multiplying by R in front of the vector/shape, we multiply the transpose of the R on the back such that is does the same operation. In which cases would we do this?


Frequently I see rotations represented by quaternion. What is the relationship with this and what is the pros and cons compared to this?