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Does the sign of the vectors returned by PCA have any significance after I center my variables?

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marked as duplicate by amoeba, Peter Flom Jan 16 '15 at 10:47

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    $\begingroup$ Short answer: no. Both the negative and the positive vectors are valid Principal Components. $\endgroup$ – Paul Hiemstra Dec 16 '11 at 8:59
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No, they are not important. From Wikipedia on SVD:

Non-degenerate singular values always have unique left and right singular vectors, up to multiplication by a unit phase factor (for the real case up to sign).

So the signs of the principal components (which correspond to singular vectors) are undetermined.

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