+- MKLab (https://mklab.gr)
+-- Forum: [INDEX] (https://mklab.gr/forumdisplay.php?fid=1)
+--- Forum: ARTFICIAL INTELLIGENCE (AI) (https://mklab.gr/forumdisplay.php?fid=5)
+---- Forum: COURSES-LECTURES (https://mklab.gr/forumdisplay.php?fid=38)
+---- Thread: Matrix Calculus for Machine Learning [MIT] (/showthread.php?tid=1212)
Matrix Calculus for Machine Learning [MIT] - mklabgr - 07-20-2026
Matrix Calculus for Machine Learning
BY MIT
Summary
Matrix Calculus for Machine Learning and Beyond is an MIT OpenCourseWare course that extends traditional calculus into the world of matrices and general vector spaces, providing the mathematical foundation behind modern machine learning and large-scale optimization. Rather than treating derivatives as collections of partial derivatives, the course emphasizes the deeper idea of differentiation as linear approximation, allowing students to work naturally with matrix-valued functions, matrix inverses, determinants, eigenvalue and singular value decompositions, and other advanced operations.
It also explains how the chain rule operates in complex computational graphs, introducing forward- and reverse-mode differentiation, backpropagation, vector-Jacobian products, and automatic differentiation—the core techniques used to train neural networks. Alongside these concepts, the course explores optimization methods such as Newton's method, Hessians, and quasi-Newton algorithms, demonstrating how advanced calculus and linear algebra combine to solve real-world scientific and engineering problems. Through lecture notes, videos, and practical examples, the course builds the mathematical intuition needed to understand the algorithms that power today's AI and data-driven technologies.
COURSE