How do you calculate the derivatives of eigenvectors and eigenvalues in matrix calculus?
In short: This lecture from the MIT course Matrix Calculus for Machine Learning and Beyond explores the mathematical techniques required to differentiate eigenvalues and eigenvectors. It provides the essential framework for handling derivatives under specific constraints.
The lecture focuses on the complexities of differentiating eigenproblems, which are fundamental to machine learning and advanced linear algebra. It specifically examines how to approach these derivatives when they are subject to constraints, such as those found on a circle or involving unitary matrices.
Part of the MIT 18.S096 course from IAP 2023, this session is taught by instructors Alan Edelman and Steven G. Johnson. It serves as a technical deep dive into the calculus of matrices, emphasizing the rigorous methods needed to compute derivatives in constrained systems.
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Sources
- Summary by Intellect · source: Lecture 8 Part 1: Derivatives of Eigenproblems
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