Matrix Methods in Data Analysis, Signal Processing, and Machine Learning | Mathematics | MIT OpenCourseWare

Course Info

Instructor

Prof. Gilbert Strang

Departments

Mathematics

As Taught In

Spring 2018

Level

Undergraduate

Topics

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Instructor Insights

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Lecture Videos

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

Course Info

Instructor

Prof. Gilbert Strang

Departments

Mathematics

As Taught In

Spring 2018

Level

Undergraduate

Topics

Learning Resource Types

Instructor Insights

Lecture Videos

Podcasts

Problem Sets

Download Course

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