How to calculate the derivative of a matrix determinant and inverse
In short: This MIT lecture explores the foundational matrix calculus required for machine learning. It covers the necessity of norms for defining derivatives and demonstrates how to derive the matrix gradient of the determinant and the Jacobian of a matrix inverse.
In this session from the 2023 IAP course 'Matrix Calculus For Machine Learning And Beyond,' instructors Alan Edelman and Steven G. Johnson explain the mathematical mechanics behind matrix differentiation. The lecture first establishes why defining a derivative requires norms for both the input and output spaces.
The core of the discussion focuses on finding the matrix gradient of the determinant function, which leads to the concept of the adjugate matrix. Additionally, the session explores the Jacobian of a matrix inverse, providing essential tools for understanding how these functions behave in high-dimensional computational contexts.
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Sources
- Summary by Intellect · source: Lecture 5 Part 1: Derivative of Matrix Determinant and Inverse
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