Hi, thanks for your post. In the equation following this sentence "This means that the variance of the dataset projected onto the first Principal", could you explain why the expression on the left is equal to the right? Thanks!

Helpful

Hi, thanks for your post, very insightful.

Could it be that the U matrix represents the PCA taking variables as vectors instead of observations?

Hi, thanks again for your post.

Could you develop mathematically the afirmation: "By dividing out the singular avlue (and multplying it by (n-1)^(1/2) to deal with the fact that we started with the covariance) we obtain a transformed dataset which is in some sense spherical"? How do you get Y = (n-1)^(1/2)*UE^-1?

Thanks

Thanks for the post. There is a mistake in Fig. 3, the dimension of $Sigma$ must be $d\times d$

Hi,

I could not figure out how did you go from $$| \tilde l_i - l_i | = O(\varepsilon \| X^TX \|) = O(\varepsilon \| X \|^2)\ $$

to this $$| \tilde \sigma_i - \sigma_i | = O(\varepsilon \frac{\| X \|^2}{\sigma_i})\,.$$

(i.e. last two equations of the post) I would appreciate if you could explain.