That was a very nice explanation. I love the rubber band analogy. But one minor qualm: A transformation, when applied, typically has several eigenvalues and eig

That was a very nice explanation. I love the rubber band analogy. But one minor qualm: A transformation, when applied, typically has several eigenvalues and eigenvectors associated with it. The "first" (usually selected as the largest, or the "principle component") eigenvector and it's associated eigenvalue is really being discussed. There are (or at least, can be) more of them! We could think about stretching the elastic along its width as well.