All Questions

The eigenfunctions of the Laplace operator on the disc can be written in polar coordinates as $f(r,\theta)=R_{nk}(r)e^{ik\theta}$, where $k\in\mathbb Z$ and $n\in\mathbb N$ and the radial function is $...

Consider the Laplacian matrix of the path graph: $$ L = \begin{bmatrix} 1 & -1 & 0 & \cdots & 0 & 0\\ -1 & 2 & -1 & \cdots & 0 & 0\\ 0 & -1 & 2 & \...

I was wondering what we can say about the eigenvectors of a matrix $A$ fullfilling $Ax =0$ where $A$ is symmetric with a diagonal equal to one and every row sums up to 0. Obviously this is a ...