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Last updated:

December 6, 2022


Unlimited Duration


This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration


Linear algebra concepts are key for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks.

This course reviews linear algebra with applications to probability and statistics and optimization–and above all a full explanation of deep learning.

Course Curriculum

  • The Column Space of A Contains All Vectors Ax Unlimited
  • Multiplying and Factoring Matrices Unlimited
  • Orthonormal Columns in Q Give Q’Q = I Unlimited
  • Eigenvalues and Eigenvectors Unlimited
  • Positive Definite and Semidefinite Matrices Unlimited
  • Singular Value Decomposition (SVD) Unlimited
  • Eckart-Young: The Closest Rank k Matrix to A Unlimited
  • Norms of Vectors and Matrices Unlimited
  • Four Ways to Solve Least Squares Problems Unlimited
  • Survey of Difficulties with Ax = b Unlimited
  • Minimizing ‖x‖ Subject to Ax = b Unlimited
  • Computing Eigenvalues and Singular Values Unlimited
  • Randomized Matrix Multiplication Unlimited
  • Low Rank Changes in A and Its Inverse Unlimited
  • Matrices A(t) Depending on t, Derivative = dA/dt Unlimited
  • Derivatives of Inverse and Singular Values Unlimited
  • Rapidly Decreasing Singular Values Unlimited
  • Counting Parameters in SVD, LU, QR, Saddle Points Unlimited
  • Saddle Points Continued, Maxmin Principle Unlimited
  • Definitions and Inequalities Unlimited
  • Minimizing a Function Step by Step Unlimited
  • Gradient Descent: Downhill to a Minimum Unlimited
  • Accelerating Gradient Descent (Use Momentum) Unlimited
  • Linear Programming and Two-Person Games Unlimited
  • Stochastic Gradient Descent Unlimited
  • Structure of Neural Nets for Deep Learning Unlimited
  • Backpropagation: Find Partial Derivatives Unlimited
  • Completing a Rank-One Matrix, Circulants! Unlimited
  • Eigenvectors of Circulant Matrices: Fourier Matrix Unlimited
  • ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule Unlimited
  • Neural Nets and the Learning Function Unlimited
  • Distance Matrices, Procrustes Problem Unlimited
  • Finding Clusters in Graphs Unlimited
  • Alan Edelman and Julia Language Unlimited

About the instructor

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Massachusetts Institute of Technology