Dynamical systems
This applet provides a visualiztion of the result of applying a matrix A multiple times. We assume A has eigenvalues lambda 1 and lambda 2 and corresponding eigenvectors eVec1 and eVec2.
The black ellipse is the parametric curve cos(th)*eVec1+sin(th)*eVec2
The green ellipse is A^n times the black ellipse
Pts is a point on the blsck ellipse with th set to s.
The red curve is the path taken by Pts
The eigenvectors are dragable. The eigenvalues, n, and s, are controlled by sliders.
As n goes from negative to positive, the green ellipse goes from being stretched in the direction of the smaller eigenvalue's vector to being stretched in the direction ot the larger eignevalue's vector