To generate a PCA from lcWGS SNPs, one may use ANGSD to generate genotype likelihoods and then use these as input to generate a covariance matrix using PCAngsd.

The covariance matrix generated by PCAngsd is a n x n matrix where n is the number of samples and p is the number of SNPs (variables). According to the [PCAngsd tutorial](http://www.popgen.dk/software/index.php/PCAngsdTutorial#Estimating_Individual_Allele_Frequencies), the principal components (i.e. the samples plotted in the space defined by the eigenvectors) can be generated directly from this covariance matrix by eigendecomposition.

This is in contrast to the 'usual' way that PCA is done (via a covariance matrix), where a p x p (not n x n) covariance matrix C is generated from a centered n x p data matrix X. Eigendecomposition of C, then generates the eigenvectors and eigenvalues. The transformed values of X into the space defined by the eigenvectors (i.e. the principal components) can then be generated through a linear transformation of X with the eigenvectors (e.g. see [this](https://stats.stackexchange.com/questions/134282/relationship-between-svd-and-pca-how-to-use-svd-to-perform-pca) excellent example).

The difference between the two methods appears to lie in the covariance matrix. With the PCAngsd method, the covariance matrix is n x n as apposed to the 'usual' p x p matrix.

So what is the difference between these two covariance matrices, and what is generated by the eigendecomposition of an n x n matrix? Is it really the sample principal components, or something else?