Eigenvalues and eigenvectors
Topics
Localization
- Localized Eigenfunctions: Here You See Them, There You Don’t
As usual, physicists know more than mathematicians in this subject, but with less certainty (this is a kind of uncertainty principle).
Intuition
Let’s think about a game. You have a matrix that transforms your vector space. The game is to find vectors that only change in size but not in direction.
Think about the simplest case. We have a matrix that just stretch x axis what could be the vectors that keep the direction under this transformation?
Let’s think about (1,1). What happens? It becomes (2,1) so it is not eigenvector.
Any vector would work because whatever vector you put, every component simply doubles.
Steven Strogatz explains how he teaches eigenvectors and eigenvalues