Matrix Methods in Data Analysis, Signal Processing, and Machine Learning (Spring 2018) (M-I-T)

• Lecture 1: The Column Space of A Contains All Vectors Ax (M-I-T)
• Lecture 3: Orthonormal Columns in Q Give Q’Q = I (M-I-T)
• Lecture 4: Eigenvalues and Eigenvectors (M-I-T)
• Lecture 5: Positive Definite and Semidefinite Matrices (M-I-T)
• Lecture 6: Singular Value Decomposition (SVD) (M-I-T)
• Lecture 7: Eckart-Young: The Closest Rank k Matrix to A (M-I-T)
• Lecture 8: Norms of Vectors and Matrices (M-I-T)
• Lecture 9: Four Ways to Solve Least Squares Problems (M-I-T)
• Lecture 10: Survey of Difficulties with Ax = b (M-I-T)
• Lecture 11: Minimizing ‖x‖ Subject to Ax = b (M-I-T)
• Lecture 12: Computing Eigenvalues and Singular Values (M-I-T)
• Lecture 13: Randomized Matrix Multiplication (M-I-T)
• Lecture 14: Low Rank Changes in A and Its Inverse (M-I-T)
• Lecture 15: Matrices A(t) Depending on t, Derivative = dA/dt (M-I-T)
• Lecture 16: Derivatives of Inverse and Singular Values (M-I-T)
• Lecture 17: Rapidly Decreasing Singular Values (M-I-T)
• Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points (M-I-T)
• Lecture 19: Saddle Points Continued, Maxmin Principle (M-I-T)
• Lecture 20: Definitions and Inequalities (M-I-T)
• Lecture 21: Minimizing a Function Step by Step (M-I-T)
• Lecture 22: Gradient Descent: Downhill to a Minimum (M-I-T)
• Lecture 23: Accelerating Gradient Descent (Use Momentum) (M-I-T)
• Lecture 24: Linear Programming and Two-Person Games (M-I-T)
• Lecture 25: Stochastic Gradient Descent (M-I-T)
• Lecture 26: Structure of Neural Nets for Deep Learning (M-I-T)