Why are there two rotations in SVD

svd

#1

Hello,

While studying about SVD I understood that u and v perform rotations whereas s performs scaling of the data.
I could not understand why there are two rotations needed.Is is something like one rotation for one axis and then another for the other axis which is orthogonal to the first axis or is there some other explanation.
Can somebody kindly explain these o me.


#2

@data_hacks-
In the SVD stage the SVD of the trajectory matrix is computed
and represented as a sum of rank-one bi-orthogonal elementary
matrices.

Hope this helps!
Regards,
hinduja1234