I am running some finite-element software on Matlab that generates solutions to the diffusion equation over a punctured, rectangular domain.
This is the same as the $k \times k$ matrix system $\textbf{Ax} = \mathbf{f}$ where $\textbf{A}$ is the 'stiffness matrix'.
The software outputs 3d plots (seen at the bottom of the page) which I presume are the eigenvectors of the diffusion equation as well as $\textbf{A}$ and $\mathbf{f}$
I am trying to calculate the eigenfunctions of the eigenvalue equation using this output from the diffusion equation. The eigenvalue equation is if the form $\textbf{Ax} = \lambda \mathbf{Qx}$. Am I wrong in thinking that the eigenvalues and corresponding eigenvectors of $\textbf{A}$ (from the diffusion equation) will also be valid for the eigenvalue equation?
