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Using matrix algebra I can calculate loadings and scores from the covariance matrix (data matrix is column centered):

covariancematrix=Covariance[data];
loadings=Eigenvectors[N[covariancematrix]];
scores1=data.Transpose[loadings];

I can obtain exactly the same scores using PrincipalComponents:

scores2=PrincipalComponents[data];
  1. my problem is about the signs of the scores values. The absolute values are the same but scores1 and scores2 can differ in the signs. Why?
  2. how can I apply the Varimax and Oblimin methods in Mathematica?
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PCA does not guarantee the sign of of the component axis, they are rotationally symmetrical. –  image_doctor Dec 6 '12 at 16:59

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