Matrix Diagonalization: Analytical insights for Numerical implementation

Abstract

Finding the eigen-systems of a (skew)symmetric matrix M that belongs to class ∈ C^{n× n} or R^{n× n} ana-lytically is a nontrvial task. The Estimations of numerical sizeof the eigen values and or the eigen vectors from the analytical estimates can be
challenging depending on the differences in the order of magnitude estimates of the elements of the matrix concerned. These details turn out to be important while constructing an uniary matrix U that would diagonalize M under similarity
transformation. Even the numerical routes to the solutions are subject to the mechine precision and cumulative round off errors for the roboustness of these estimates