Hello,
I have a short question about the prcomp function. First I cite the
associated help page (help(prcomp)):
"Value:
...
SDEV the standard deviations of the principal components (i.e., the square
roots of the eigenvalues of the covariance/correlation matrix, though the
calculation is actually
I think PCA decomposes matrix A according to A'A, not to COV (A).
But if A is centered then A'A = (n + 1) COV (A).
So for non-centered A, you want to look at A'A instead:
> crossprod(A) %*% evec[,1] / (nrow (A) - 1) - eval [1] * evec [,1]
[,1]
[1,] 0.000e+00
[2,] 0.000e+00
[3,] 1.066e
Dear Claudia,
you are right. Thank you very much for your explanations. So in the
non-centered case SDEV does not contain the "square roots of the eigenvalues
of the covariance/correlation matrix". In in the centered case it holds
A´A=(n-1)*cov(A) (not n+1).
Have a nice day.
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