Hi again! You are right, as I was following the article and the both equations have M or /sqrt(M) and then they call the covariance matrix as the correlation matrix when the difference between covariance matrix and correlation matrix is because the correlation matrix is a normalized form from covariance matrix. :)

sorry I wrote wrong, actually is srqt(M), as the article that I wrote as references, but it does not matter because it will cancel in the thrd equation. Anyway thank you so much for you aswer, it helps me a lot!!! Best regards!

Thanks @adriculteur. Than I do not need substract the zero-mean and std deviation that I did for the training set from the validation/test set? just multiply the validation/test dataset with the eigenvectors and it is done?