Norms and Inequalities
Measuring size, distance, and stability in vector and matrix spaces through norms and their fundamental inequalities.
Matrix Decompositions
Canonical matrix decompositions and variational characterizations that underpin dimensionality reduction, optimization, and spectral methods
Asymptotic Notation and Stochastic Convergence
Standard asymptotic notation and probabilistic limit tools for analyzing convergence, consistency, and stochastic approximation.
Random Projections
Random linear embeddings and geometric principles for dimension reduction in high-dimensional spaces.
Matrix Concentration and Perturbation Inequalities
Probabilistic inequalities and perturbation bounds governing the behavior of random matrices and their spectra.
