I am trying to get some intuition regarding the U and V matrices in SVD ($M=UEV^T$). I think these are orthonormal basis vectors, but I am struggling to get an intuition if they represent anything more than matrix transformations.
For example, in NMF, I understand that the decomposed matrices can be combined as a linear combination of basis vectors in one matrix with weights in the other matrix. In PCA, I understand that the eigenvectors have real significance in representing orthogonal axes of maximal variation, defined by the eigenvalues. But in SVD, I don't see any immediate connection.
Could someone enlighten me?