CHAPTER 08-PCA FROM SCRATCH

I have a question, why are you applying a SVD on a zero-mean (along the first axis) matrix? I'm not sure that's correct, I think you need to apply the SVD to the covariance matrix.
In fact, when checking the pca.explained_variance_ratio_, that corresponds only to component of the vector S returned by the SVD (normalized to the sum of elements in the vector) applied on a covariance matrix.