  We prove the method of power iteration for matrices with at most finite
entries from the Levi-Civita field $\mathcal C$ under the assumption that there
exists an eigenvalue with the strictly largest in absolute value complex part.
In this case the weak convergence of a start vector to the eigenvector, that
corresponds to the largest eigenvalue, is proven. Further, we prove that the
Rayleigh quotient of the largest eigenvector also converges weakly to the
corresponding eigenvalue. As a corollary, the same holds for matrices and
polynomials over the Puiseux series field. In addition to that, we deliver an
implementation of our method in Python.
