# Fast principal component analysis

I'd like to speed up a principal value value analysis. The data contains a large set of vectors with a large dimension. Both are in the range of 1000. I want to obtain the loadings matrix for further calculations. The "Eigenvectors" part takes most of the computation time.

lMat = Table[RandomReal[], {i, 1000}, {j, 2000}];
mwVec = Mean[lMat];
lVerMat = (# - mwVec) & /@ lMat (* translation to the mean *);
covarMat = Covariance[lVerMat];