SVD is the decomposition of a matrix into two rotation matrices and a scaling matrix, by definition:

https://en.wikipedia.org/wiki/Singular_value_decomposition

i don't understand who is having trouble reading the dialogue here you or i;

> there is absolutely no sense in which the SVD/PCA decomposition is just a rotation matrix... (hint: scaling is extremely important)

...

> SVD is the decomposition of a matrix into two rotation matrices and a scaling matrix, by definition:

yes that's exactly what i was implying when i said SVD more than just rotation, scaling is also important.

my point, which is my same original point, is that if you think learning about rotation/euler matrices is going to prepare you in any way, shape, or form for ML (vis-a-vis SVD/PCA or RoPE or anything else) you're in for a very rude awakening.