Applications related to artificial intelligence, machine learning, and system identification simulations essentially use eigenvectors. Calculating eigenvectors for very large matrices using conventional methods is compute-intensive and renders the applications slow. Recently, Eigenvector-Eigenvalue Identity formula promising significant speedup was identified. We study the algorithmic implementation of the formula against the existing state-of-the-art algorithms and their implementations to evaluate the performance gains. We provide a first of its kind systematic study of the implementation of the formula. We demonstrate further improvements using high-performance computing concepts over native NumPy eigenvector implementation which uses LAPACK and BLAS.