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An immersive linear algebra textbook with interactive figures, covering vectors, matrices, determinants, eigenvalues, and more.
A historical account of the development of the singular value decomposition (SVD) up to 1993, tracing its origins and key contributions. The paper is a classic reference for the mathematical underpinnings of many modern data analysis and machine learning techniques.
This article examines the equivalence between the component and geometric definitions of the vector dot product in Euclidean space, providing a geometric proof using the law of cosines and a projection proof using orthonormal basis vectors.
This blog post explains how to derive the Singular Value Decomposition (SVD) from scratch by focusing on the underlying intuition and the motivation behind the concept, arguing that traditional math books often present formalized conclusions without showing the exploratory path.
Gilbert Strang presents an updated vision for teaching linear algebra through a YouTube playlist and MIT OpenCourseWare site.
A Twitter thread shares a curated list of 10 free, legally downloadable textbooks from MIT, Stanford, Berkeley, and Harvard, covering topics like linear algebra, machine learning, probability, and data science.
A tweet announces that University of Michigan's ROB 501, a 26-lecture series covering the mathematical foundations of robotics, is available for free on YouTube with open-source materials on GitHub.
University of Michigan Robotics shares free open-source course materials including lectures, textbooks, and projects from their top robotics program, covering topics from computational linear algebra to autonomous systems.
The University of Michigan has made its entire robotics degree curriculum freely available on GitHub, including lecture videos, textbooks, and assignments, starting with practical linear algebra for robotics.
A tweet showcasing a CuTe DSL kernel sample that uses layouts to express transposition, part of the FlashAttention-4 kernel.
A curated GitHub collection (Mathematics for Machine Learning) that organizes books, papers, video lectures, and math basics for learning the math behind machine learning, covering linear algebra, calculus, probability, statistics, and more.
Introduces LinAlg-Bench, a diagnostic benchmark evaluating 10 frontier LLMs on structured linear algebra computation across matrix dimensions, revealing that LLM mathematical failure is structurally constrained and transitions from execution errors to computational abandonment at 4x4 scale.
Terence Tao states that the mathematics underlying modern LLMs is simple, using basic linear algebra and calculus, but the unpredictability of model performance across tasks remains a mystery due to the complex nature of natural language data.
This paper presents a parallelization framework for CFR algorithms using linear algebra operations, achieving up to four orders of magnitude speedup on GPU compared to CPU implementations.
Think Linear Algebra is a code-first, open-source educational resource that teaches linear algebra concepts using Python and Jupyter notebooks, focusing on practical applications rather than abstract theory.