Lecture 1: The Column Space of A Contains All Vectors Ax
52:14Lecture 2: Multiplying and Factoring Matrices
48:253. Orthonormal Columns in Q Give Q'Q = I
49:244. Eigenvalues and Eigenvectors
48:555. Positive Definite and Semidefinite Matrices
45:276. Singular Value Decomposition (SVD)
53:337. Eckart-Young: The Closest Rank k Matrix to A
47:16Lecture 8: Norms of Vectors and Matrices (18.065)
49:21Lecture 9: Four Ways to Solve Least Squares Problems (18.065)
49:51Lecture 10: Survey of Difficulties with Ax = b (18.065)
49:36Lecture 11: Minimizing "x" Subject to Ax = b (18.065)
50:22Lecture 12: Computing Eigenvalues and Singular Values (18.065)
49:28Lecture 13: Randomized Matrix Multiplication (18.065)
52:24Lecture 14: Low Rank Changes in A and Its Inverse (18.065)
50:34Lecture 15: Matrices A(t) Depending on t, Derivative = dA/dt (18.065)
50:52Lecture 16: Derivatives of Inverse and Singular Values (18.065)
43:08Lecture 17: Rapidly Decreasing Singular Values (18.065)
50:34Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points (18.065)
49:00Lecture 19: Saddle Points Continued, Maxmin Principle (18.065)
52:13Lecture 20: Definitions and Inequalities (18.065)
55:01Lecture 17: Rapidly Decreasing Singular Values (18.065)
Guest lecturer Alex Townsend explains why low rank matrices are prevalent in computational mathematics and their critical role in applications like image compression.
MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018
Instructor: Alex Townsend
View the complete course: https://ocw.mit.edu/18-065S18
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63oMNUHXqIUcrkS2PivhN3k
Lecture 16: Derivatives of Inverse and Singular Values (18.065)
Next · Lecture 18Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points (18.065)