Eigenvalue theory is a cornerstone of applied mathematics, playing a fundamental role in stability analysis, control theory, computational methods, and engineering applications. This volume explores the interplay between theoretical insights and real-world implementations, demonstrating how eigenvalue-based techniques drive advancements in modern engineering. Covering topics such as numerical linear algebra, spectral analysis, high-performance computing, and data-driven methodologies, this collection presents innovative approaches for solving complex eigenvalue problems in control systems, structural analysis, machine learning, and large-scale simulations alongside cutting-edge numerical methods that enhance computational efficiency and accuracy. By bridging mathematical theory with engineering practice, this book is a valuable resource for researchers, engineers, and practitioners looking to apply eigenvalue techniques in scientific computing, optimization, and emerging technologies.