"Matrix Differential Calculus for Machine Learning and Beyond" is a free course of lecture materials from MIT, focusing on the mathematics of derivatives of vectors and matrices.

The materials cover gradients, Jacobians, derivatives of matrix functions, differentials, derivatives of matrix products, inverse matrices, and determinants, Kronecker products, optimization, and automatic differentiation. It also explores the application of these methods in machine learning.

In my opinion, this is a valuable resource for those who are already familiar with the basics of linear algebra and mathematical analysis and want to understand how differentiation is generalized to vectors and matrices and applied in modern optimization problems.

https://ocw.mit.edu/courses/18-s096-matrix-calculus-for-machine-learning-and-beyond-january-iap-2023/mit18_s096iap23_lec_full.pdf

https://t.me/MachineLearning9