Suppose that you are driving a car and you are hit with a big tree. The main eigenvector is in the direction from the car to the tree, the eigenvalue measures

Suppose that you are driving a car and you are hit with a big tree. The main eigenvector is in the direction from the car to the tree, the eigenvalue measures the deformation of the car produced by this accident. If the car is a half shorter after the accident then the eigenvalue is 1/2.