I understand how to calculate all three of these, but what is their physical function. How do they physically manipulate the environment we are trying to describe through mathematics? Please don't use any formulas to explain this. The formulas are easy, the physical meaning is what I'm missing. To the best of my understanding, Eigenfunctions return a topology/manifold/etc. to it's original position. Eigenvectors expand or compress a tensor/matrix. Eigenvalues give the general rest position of a linear equation. I believe I'm misunderstanding something.