You are wrong. No covariance matrix is computed. Please don't "speculate" --
read the Help file which clearly states:

"The calculation is done by a singular value decomposition of the (centered
and possibly scaled) data matrix, not by using eigen on the covariance
matrix. This is generally the preferred method for numerical accuracy. "

-- Bert Gunter

> I speculate that the underlying function transposes the 
> input data matrix and computes the the TxT [rather than SxS]
> covariance matrix and solves for the eigenvalues/vectors. 
> It then uses a linear transformation to get the results
> for the original input data matrix.
> 
> Computationally, the above is much faster and uses less memory.
> 
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