[R] Confused by SVD and Eigenvector Decomposition in PCA

[Feng Zhang]

Hey, All

In principal component analysis (PCA), we want to know how many percentage
the first principal component explain the total variances among the data.

Assume the data matrix X is zero-meaned, and
I used the following procedures:
C = covriance(X) %% calculate the covariance matrix;
[EVector,EValues]=eig(C) %%
L = diag(EValues) %%L is a column vector with eigenvalues as the elements
percent = L(1)/sum(L);


Others argue using Sigular Value Decomposition(SVD) to
calculate the same quantity, as:
[U,S,V]=svd(X);
L = diag(S);
L = L.^2;
percent = L(1)/sum(L);


So which way is the correct method to calculate the percentage explained by
the first principal component?

Thanks for your advices on this.

Fred