# Is it possible to get the transformation PrincipalComponents uses to transform data?

As far as I can see PrincipalComponents[data] just gives data in the principal component basis. The problem is that after this, I would like to transform new data into the same basis, which requires that I know the actual principal components.

There is the option of calculating Eigenvectors[Covariance[data]] (given the data is centered on the origin) but for the eigenvectors I get this way the signs are usually different from the ones that the PrincipalComponents[] function uses.

Is there an easy way of getting the actual transformation used or transforming new data into the PC basis of the previous dataset?

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