I've been reading about principal components and residual matrixs. It's my understanding if you used every principal component to recalculate your orginal data, then the residual matrix should be 0. Therefore, I created a fake dataset of two random variables and calculated the principal components. When I do eigenvector1,1*princomp1,1+Eigenvector1,2*princomp1,2 = var 1 similarly When I do eigenvector2,1*princomp2,1+Eigenvector2,2*princomp2,2 = var 2 so therefore the residual matrix is 0 which is what I wanted. However, this is only true when I standardize the data. If I don't standardized the data, the two formulas I listed above aren't true. What is throwing me for a loop is none of the papers I read said anything about standardizing the data, but it looks like the data must be standardized for this to hold. I don't want to make any assumptions so I thought I would ask. Is this correct?