Norms and Inequalities
Vector and matrix norms, their ordering and duality, and the standard inequalities between them.
Matrix Decompositions
Spectral, SVD, polar, QR, and Schur decompositions, with Courant-Fischer and Eckart-Young.
Asymptotic Notation and Stochastic Convergence
Big-O and little-o, their stochastic versions, modes of convergence, Slutsky, the law of large numbers, and the CLT.
Random Projections
Johnson-Lindenstrauss and subspace embeddings: why a random linear map preserves distances, and how few dimensions it needs.
Matrix Concentration and Perturbation Inequalities
Hanson-Wright, matrix Bernstein, Weyl, and Davis-Kahan, and how they combine in low-rank plus noise models.
