Non-Asymptotic Random Matrix Theory
Lecture 1:
Background, Techniques, Methods
Lecture 2:
Concentration of Measure
Lecture 3:
Concentration of Measure (cont'd)
Lecture 4:
Dimension Reduction
Lecture 5:
Subgaussian Random Variables
Lecture 6:
Norm of a Random Matrix
Lecture 7:
Largest, Smallest, Singular Values of Random Rectangular Matrices
Lecture 8:
Dudley's Integral Inequality
Lecture 9:
Applications of Dudley's Inequality - Sharper Bounds for Random Matrices
Lecture 10:
Slepian's Inequality - Sharpness Bounds for Gaussian Matrices
Lecture 11:
Gordon's Inequality
Lecture 12:
Sudakov's Minoration
Lecture 13:
Sections of Convex Sets via Entropy and Volume
Lecture 14:
Sections of Convex Sets via Entropy and Volume (cont'd)
Lecture 15:
Invertibility of Square Gaussian Matrices, Sparse Vectors
Lecture 16:
Invertibility of Gaussian Matrices and Compressible/Incompressible Vectors
Lecture 17:
Invertibility of Subgaussian Matrices - Small Ball Probability via the Central Limit Theorem
Lecture 18:
Strong Invertibility of Subgaussian Matrices and Small Ball Probability via Arithmetic Progression
Lecture 19:
Small Ball Probability via Sum-Sets
Lecture 20:
The Recurrence Set (Ergodic Approach)