In linear algebra rotations are represented by matrices, i.e. linear transformations
But this page is very interesting
it vaguely talks about rotations as being quadratic in the way that the length of a vector is quadratic
then it also shows how a rotation takes in something quadratic and spits out something linear
but it also vaguely hints that the 'quadratic-ness' as being encoded in rotating your basis vectors
Is there a way to make all this precise with rigorous linear operators, bilinear and quadratic forms etc...?
It's very hand-wavey, but cool if correct.
I'm guessing this 'quadratic' business means tensors, bilinear forms etc... so I guess they're saying that all the rotation matrices, unitary geometry etc... is properly thought of as part of bilinear algebra rather than linear algebra - make sense?