Learn · Matrix Methods in Data Analysis, Signal Processing, and Machine Learning
Lecture 10 of 34Video Lectures50 min
Lecture 10: Survey of Difficulties with Ax = b
Prof. Gilbert Strang · Massachusetts Institute of Technology
Credits and licence
- From
- Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Massachusetts Institute of Technology (at MIT OpenCourseWare)
- Licence
- CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only.
- Attribution
- Prof. Gilbert Strang. Matrix Methods in Data Analysis, Signal Processing, and Machine Learning. Spring 2018. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
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- Tweens profiles and older. How courses are placed
All the lectures
- Lecture 1: The Column Space of A Contains All Vectors Ax
- Lecture 2: Multiplying and Factoring Matrices
- Lecture 3: Orthonormal Columns in Q Give Q’Q = I
- Lecture 4: Eigenvalues and Eigenvectors
- Lecture 5: Positive Definite and Semidefinite Matrices
- Lecture 6: Singular Value Decomposition (SVD)
- Lecture 7: Eckart-Young: The Closest Rank k Matrix to A
- Lecture 8: Norms of Vectors and Matrices
- Lecture 9: Four Ways to Solve Least Squares Problems
- Lecture 10: Survey of Difficulties with Ax = b
- Lecture 11: Minimizing ‖x‖ Subject to Ax = b
- Lecture 12: Computing Eigenvalues and Singular Values
- Lecture 13: Randomized Matrix Multiplication
- Lecture 14: Low Rank Changes in A and Its Inverse
- Lecture 15: Matrices A(t) Depending on t, Derivative = dA/dt
- Lecture 16: Derivatives of Inverse and Singular Values
- Lecture 17: Rapidly Decreasing Singular Values
- Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points
- Lecture 19: Saddle Points Continued, Maxmin Principle
- Lecture 20: Definitions and Inequalities
- Lecture 21: Minimizing a Function Step by Step
- Lecture 22: Gradient Descent: Downhill to a Minimum
- Lecture 23: Accelerating Gradient Descent (Use Momentum)
- Lecture 24: Linear Programming and Two-Person Games
- Lecture 25: Stochastic Gradient Descent
- Lecture 26: Structure of Neural Nets for Deep Learning
- Lecture 27: Backpropagation: Find Partial Derivatives
- Lecture 30: Completing a Rank-One Matrix, Circulants!
- Lecture 31: Eigenvectors of Circulant Matrices: Fourier Matrix
- Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule
- Lecture 33: Neural Nets and the Learning Function
- Lecture 34: Distance Matrices, Procrustes Problem
- Lecture 35: Finding Clusters in Graphs
- Lecture 36: Alan Edelman and Julia Language