[SciPy-user] getting the "best" two eigenvectors for a PCA analysis with a power method

Robert Kern rkern at ucsd.edu
Thu Sep 1 00:02:23 CDT 2005

Noel O'Boyle wrote:
> R calculates the PCs using singular value decomposition, instead of
> using the eigenvalues of the covariance matrix.

Another reason to use the SVD instead of an eigenvector decomposition of
the covariance matrix: strictly speaking, there's no such thing as an
eigenvector decomposition of a covariance matrix. The eigenvector
decomposition is only defined for linear automorphisms, which map a
space onto itself. Covariance matrices map a space onto its dual.

Robert Kern
rkern at ucsd.edu

"In the fields of hell where the grass grows high
 Are the graves of dreams allowed to die."
  -- Richard Harter

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