I've been reading about principal components and residual matrixs.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Principal Components and the Residual Matrix

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