A First Course in Random Matrix Theory: for Physicists, Engineers and Data Scientists 1st Edition

Physicists and engineers view the real world through the lenses of data, models, and algorithms. Data inherently carries noise, and traditional statistical methods have historically coped well with moderate levels of randomness. However, the advent of Big Data and the computational capabilities necessary to analyze them have made classical tools obsolete. Emerging tools like random matrix theory and the study of large sample covariance matrices are now essential for processing vast datasets and understanding modern deep learning algorithms.

This book introduces the fundamentals of random matrices, extending conventional concepts of probabilistic independence to non-commuting random variables. It emphasizes modern advancements in matrix theory and includes practical examples and applications in financial engineering and portfolio construction. This unique resource is indispensable for physicists, engineers, data analysts, and economists seeking to navigate and harness the potential of contemporary data-driven methodologies.