How to simplify complex matrix derivatives using the power of Kronecker products
In short: This lecture from MIT's 2023 Matrix Calculus course explains how to transform matrix-function derivatives into standard Jacobian matrices. It is essential viewing for anyone looking to bridge the gap between abstract linear operators and the practical matrix computations used in machine learning.
Matrix-function derivatives are fundamentally linear operators acting on matrices. While this is mathematically elegant, it can be difficult to compute directly. This lecture demonstrates how to leverage Kronecker products to convert these operators into more familiar Jacobian matrices.
By reframing these derivatives, the course provides a clearer path for performing calculations in machine learning contexts. The material is part of the 18.S096 course, Matrix Calculus For Machine Learning And Beyond, taught by Alan Edelman and Steven G. Johnson.
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Sources
- Summary by Intellect · source: Lecture 3 Part 1: Kronecker Products and Jacobians
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