What the eigenvalues of a large random matrix do: the empirical spectral distribution and Wigner's semicircle law reached by the moment method, the Gaussian ensembles and the Dyson index, the joint eigenvalue density and the level repulsion hidden in its Vandermonde factor, Wishart matrices and the Marchenko-Pastur law, Tracy-Widom edge statistics, the BBP phase transition that decides when a real signal is visible at all, the circular law and non-normality, free probability, universality, Dyson Brownian motion, determinantal processes, random graph spectra, and what all of it says about principal component analysis in high dimensions.
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Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the moment just before you'd forget it. A short placement check finds what you already know, so you start Random Matrix Theory exactly where it's useful.