I understand that the the eigenvalues of the Fisher Information Matrix (FIM) represent the magnitude of the spread in the direction of the principal components.
By the way, I am curious if there are any relationships between the rows/columns (hence the parameters) of the FIM and the elements of the related eigenvectors. For instance, let's say I have a NxN FIM so the eigenvectors have N elements each. Can I say that the i-th element of the j-th eigenvector corresponds to the i-th row/column of the FIM?
Thank you!