I had to find the eigenvectors and eigenvalues of a $50\times 50$ matrix of the form
$$ A = \begin{pmatrix} 2 & -1 & && \\ -1 &2 &-1 && \\ & \ddots & \ddots &\ddots & \\ &&-1&2&-1 \\ &&& -1& 2 \end{pmatrix} $$
and plot the values of the vector components over the vector components itself for the four smallest eigenvalues $\lambda$. What I got was the following graph, which suprised me:
eigenvectorcomponentsvalues over eigenvectorcomponents
The $\lambda's$ are the eigenvalues. I do not understand, why the graphs have the form of sinus-like functions and which kind of polynomials these are. My supervisor already said, that these are no trigonometric functions. Does one know a reason for that?
