# How to correctly normalize modulus and phase of an eigenvector?

I am solving a linear stability problem using finite element discretization. Then, I have a generalised eigenvalue problem: $$\lambda M x = J x.$$ I obtain complex eigenvalue and eigenvectors from Arpack using inverse shift method. I would like to compare the eigenvectors obtained with different meshes. To do this it is necessary to normalize norm and phase in a proper way. As concerns the norm of the eigenvector I normalize it imposing: $$x^HMx = 1.$$ Now, I would need an integral norm for the phase too. I tried one but it doesn't seem to work. I cannot obtain similar eigenvectors with two different meshes.