I have 4 standard normal features on which I perform PCA. I then take the first principal component (with all of the components). Is it possible to a priori say what is the max and the min value that the transformed series will have?
I guess, if we assume that the original standard normal features never exceed +/- 5, then the max of the final transformed series would be the PCA coefficients product summed by 5? But is it possible that the PCA coefficients are [1, 1, 1, 1] in this case? Or is there some sort of a bound on what the PCA coefficients can be?