Eigenvalues Wiggle

We see the roots of a polynomial which changes in time. We see the eigenvalue repulsion. If eigenvalues are close to each other, they want to get away from each other. Collisions can happen but they happen rarely. In the pictures we see a deformation of the polynomial. The deformation parameter is t.

Direct Media Links: Webm, Ogg Ipod	Direct Media Links: Webm, Ogg Ipod
Roots of x22 + 22 sin(t) x11 = 1	x22 + 10 sin(2 t) x11-8cos(3 t) x3 + 6 sin(4 t) x = 1

In the following case we took some random polynomial p(x)=x⁵⁰ + ∑_k=0<sup>40 a_k sin(k t) x(k-1)= 1 where t is a parameter. We see that the roots are still quite close to the 50'th roots of unity on the circle. But they move around a bit. Still, we see the eigenvalue repulsion.

Direct Media Links: Webm, Ogg Ipod</sup>