Lecture Videos | Matrix Calculus for Machine Learning and Beyond | Mathematics | MIT OpenCourseWare

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Mathematics

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January IAP 2023

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Undergraduate

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Mathematics

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Lecture Videos

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

Course Info

Instructors

Departments

Mathematics

As Taught In

January IAP 2023

Level

Undergraduate

Topics

Mathematics

Learning Resource Types

Lecture Videos

Lecture Notes

Readings

Instructor Insights

Editable Files

Problem Sets

Problem Set Solutions

Download Course

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