# Is the sign of principal components meaningless? [duplicate]

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

• Short answer: no. Both the negative and the positive vectors are valid Principal Components. – Paul Hiemstra Dec 16 '11 at 8:59

## 1 Answer

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.