Small correction: eigenfunctions are analogous to eigenvectors, not eigenvalues. In fact they _are_ eigenvectors, in the sense that they are vectors in a vector

Small correction: eigenfunctions are analogous to eigenvectors, not eigenvalues. In fact they _are_ eigenvectors, in the sense that they are vectors in a vector space of functions (or some restricted set of functions, e.g. continuous functions or periodic functions).