I have two matrices a, b of dimensions (100x500), (100x15000) and I am trying to find associations between sets of variables in both matrices.
When I perform principal component analysis on matrix a, the highest loadings of the first principal component corresponds to a set of variables which contribute towards the largest proportion of variability in this dataset. These variables are of interest in my research and I would like to determine which variables in dataset b are associated with this principal component.
Therefore my question is: If I perform principal component analysis on matrix b, can I perform correlations between the eigenvectors of a and the eigenvectors of b to determine if an association between these two datasets exists?
If such a correlation does exist, what exactly does a correlation between eigenvectors actually represent?