I'm using Mathematica's
PrincipalComponents to do a principal components analysis on a data set with m data points and n variables (m > n). The command produces the m by $n$ matrix which contains the representation of each of the data in the principal components basis.
My question is -- how can I instead extract the principal component vector itself, as coefficients of original variable basis vectors? I'm aware you can do this with singular value decomposition or calculating the eigenvectors of the covariance matrix, but in doing those calculations there is an arbitrary choice of sign involved which might not be the same choice as
PrincipalComponents. I want to see exactly the principal component vectors used by