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Browse materialsMIT 18.S096 · January IAP 2023

Matrix Calculus for Machine Learning and Beyond

Subjects: Algebra · Calculus · Linear Algebra · Machine Learning · Mathematics

Art: Anonymous painter,15th century, Westerner and Arab practicing geometry 15th century manuscript, 15th… · Public domain

Instructors: Prof. Alan Edelman, Prof. Steven G. Johnson
Term: January IAP 2023
Level: Undergraduate
What's inside: 17 videos · 2 problem sets · 4 solutions · 2 lecture notes · 43 other files · 3 web pages
Materials open: Videos here · files on MIT OCW

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About this course

Source: MIT OpenCourseWare 18.S096 Matrix Calculus for Machine Learning and Beyond, January IAP 2023, Prof. Alan Edelman, Prof. Steven G. Johnson — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.

Has MIT solutions 5 files in this course are named by MIT as solutions.

Before you start

Prerequisites are not listed here. Check MIT's own syllabus for this course.

How this course was organized

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Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Syllabus

Full Lecture Notes: Matrix Calculus for Machine Learning and BeyondPDF Download

Lecture Notes and Readings

21 files

Problem Sets

11 files

Other materials from this course

17 video transcripts

MIT OpenCourseWare, Prof. Alan Edelman, Prof. Steven G. Johnson, 18.S096 Matrix Calculus for Machine Learning and Beyond, January IAP 2023.

License: CC BY-NC-SA 4.0 · Edition: January IAP 2023 · Open the original course on OCW ↗

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Matrix Calculus for Machine Learning and Beyond

Before you start

What's here, and what isn't

Not included here

Materials by section

Syllabus

Lecture Notes and Readings

Problem Sets

Other materials from this course

Lecture 1 Part 1: Introduction and Motivation

Lecture 1 Part 2: Derivatives as Linear Operators

Lecture 2 Part 1: Derivatives in Higher Dimensions: Jacobians and Matrix Functions

Lecture 2 Part 2: Vectorization of Matrix Functions

Lecture 3 Part 1: Kronecker Products and Jacobians

Lecture 3 Part 2: Finite-Difference Approximations

Lecture 4 Part 1: Gradients and Inner Products in Other Vector Spaces

Lecture 4 Part 2: Nonlinear Root Finding, Optimization, and Adjoint Gradient Methods

Lecture 5 Part 1: Derivative of Matrix Determinant and Inverse

Lecture 5 Part 2: Forward Automatic Differentiation via Dual Numbers

Lecture 5 Part 3: Differentiation on Computational Graphs

Lecture 6 Part 1: Adjoint Differentiation of ODE Solutions

Lecture 6 Part 2: Calculus of Variations and Gradients of Functionals

Lecture 7 Part 1: Derivatives of Random Functions

Lecture 7 Part 2: Second Derivatives, Bilinear Forms, and Hessian Matrices

Lecture 8 Part 1: Derivatives of Eigenproblems

Lecture 8 Part 2: Automatic Differentiation on Computational Graphs