Adoption of spectral analysis as a mainstream tool for portfolio management has languished despite the growing body of academic research. The highly theoretical nature of the recent publications have slowed the application of spectral analysis to specific use cases. In this paper, we show a step-by-step approach, advantages and results of spectral decomposition in portfolio reallocation. Specifically, we show how spectral decomposition solves two of the most pressing large-scale portfolio reallocation problems: extreme weights and transaction costs. We further show the empirical results of portfolio reallocation under different common portfolio composition scenarios, and how spectral decomposition helps speed up and outperform traditional portfolio allocation techniques.