# Solve Simple Eigenvalue Equation over 2D Mesh (no FEM)

Hi,

I apologize for this question, but I wanted to make sure I understand how to solve a simple eigenvalue equation over a 2D mesh using NGSolve. The goal is to get eigenvalues and eigenvectors at each point of the mesh, with the intention of doing more post-processing later. Let’s say I have some generally complex-valued 2x2 matrix A(x,y), and I simply want to calculate V and \lambda in the eigenvalue equation: A V = \lambda V. If A is Hermitian, \lambda are real, and V are generally complex-valued.
Since there’s no FEM yet, I could easily do this using NumPy’s linalg(), but I want to see how it can be done using NGSolve. I would want to calculate each V(x,y) and \lambda(x,y) and plot the latter over the mesh. Ultimately, I will be taking derivatives of V and taking dot products, but I want to get this first step down.
Is there a minimal example I could use for reference? I saw some articles and posts about PINVIT, but I want to make sure I am not over-complicating things.

Thank you!