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.

翻译：我们证明了在Levi-Civita域 $\mathcal C$ 上具有至多有限项的矩阵的幂迭代法，其前提是存在一个绝对值复数部分严格最大的特征值。在此情况下，证明了起始向量弱收敛于对应于最大特征值的特征向量。进一步，我们证明了最大特征向量的瑞利商也弱收敛于相应的特征值。作为推论，对于Puiseux级数域上的矩阵和多项式，上述结论同样成立。此外，我们提供了该方法在Python中的实现。