Summary

This chapter was about random matrices. What started out sounding like an esoteric plaything of mathematicians turned out to be a commonly occurring concept in data science with many applications. The tools to study random matrices come from RMT. These tools can be very mathematically advanced, so we have only given an overview of the main results of RMT and what the implications of those results are. We did not attempt to go into the derivations of those results. However, we had to learn about several new concepts. Those new concepts include the following:

• A random matrix is a matrix whose matrix elements are drawn from a distribution
• Random matrices are studied using RMT
• Large random matrices can display universal behavior
• A large-scale interacting system can be modeled as a large random matrix
• The Wigner semicircle law
• The GOE, GUE, and GSE families of matrices
• The Marčenko-Pastur distribution
• The bulk of the eigenvalues of a sample...