I am very new to PCA and I was trying, just as excercize, to reconstruct original dataset from loadings.
Let's suppose I have a matrix A corresponding to the original dataset and C that is the z-score of matrix A. What I want to do is to get back matrix A starting from loadings and C as A=C L' where L is the matrix of loadings (as described here: How to interpret PCA loadings?). So after doing the PCA I calculated the loading matrix L by multiplying each column of the eigenvectors matrix for its eigenvalue square root (i.e. first column by first sqrt eigenvalue, second column by second sqrt eigenvalue...). However when I calculated C L' I got a new matrix different from A.
Where do I go wrong? Tried to search around but could not find anything.