Hacker News with Generative AI: Linear Algebra

Matrix Calculus (For Machine Learning and Beyond) (arxiv.org)
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and return a matrix inverse or factorization, derivatives of ODE solutions, and even stochastic derivatives of random functions.

Machine Learning, Calculus, Linear Algebra, Mathematics

181 points by ibobev 4 days ago | 30 comments

Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares (web.stanford.edu)
This book is used as the textbook for our own courses ENGR108 (Stanford) and EE133A (UCLA), where you will find additional related material.

Linear Algebra, Mathematics, Education, Computer Science, Engineering

7 points by ibobev 9 days ago | 0 comments

Geometric Algebra (bivector.net)
Clifford's Geometric Algebra enables a unified, intuitive and fresh perspective on vector spaces, giving elements of arbitrary dimensionality a natural home.

Mathematics, Geometry, Linear Algebra

200 points by agnishom 35 days ago | 61 comments

Math books like Infite Powers or Calculus Made Easy but for other topics? (ycombinator.com)
I recently read the above because I wanted to refresh my calculus skills and they were exactly the level and depth for a busy software engineer. Do you have other examples of foundational math books that are readable for the interested layman, e.g. for linear algebra?

Mathematics, Books, Linear Algebra, Software Engineering

13 points by leandot 52 days ago | 10 comments

What Is a Bivector? [video] (youtube.com)

Mathematics, Videos, Linear Algebra

5 points by jfantl 58 days ago | 0 comments

The Tensor Cookbook (2024) (tensorcookbook.com)
This book aims to standardize the notation for tensor diagrams by rewriting the classical "Matrix Cookbook" using this notation.

Mathematics, Linear Algebra, Tensor Notation, Scientific Computing, Computer Science

199 points by t55 61 days ago | 37 comments

Anatomy of a Formal Proof (ams.org)
It has been a long day and you are making your way through a paper related to your work. You suddenly come across the following remark: “…since $x$ and $y$ are eigenvectors of $f$ with distinct eigenvalues, they are linearly independent.” Wait—how does the proof go? You should really know this. Here $x$ and $y$ are nonzero elements of a vector space $V$ and $f : V to V$ is a linear map.

Mathematics, Linear Algebra, Proofs

134 points by bikenaga 68 days ago | 11 comments

Beating cuBLAS in Single-Precision General Matrix Multiplication (salykova.github.io)
This project is inspired by the outstanding works of Andrej Karpathy, George Hotz, Scott Gray, Horace He, Philippe Tillet, Jeremy Howard, Lei Mao and the best CUDA hackers from the GPU MODE community (Discord server). A special thanks to Mark Saroufim and Andreas Köpf for running GPU MODE and all you’ve done for the community.

GPU Computing, Machine Learning, Linear Algebra, Performance Optimization

98 points by skidrow 78 days ago | 8 comments

Robotics 101 at UMich: Applied numerical linear algebra as intro linear algebra (robotics.umich.edu)
Computational Linear Algebra is a pilot first-semester, first-year undergraduate course that will show how mathematics and computation are unified for reasoning about data and making discoveries about the world.

Robotics, Education, Linear Algebra, Mathematics, Computation

296 points by jamesliudotcc 85 days ago | 73 comments

Einsum in Depth (joelburget.com)

Mathematics, Linear Algebra, Python

87 points by joelburget 89 days ago | 31 comments

How I used linear algebra to build an interactive diagramming editor (medium.com)
Ah, matrices. One of those core linear algebra concepts we all encountered in school. Despite their significance, I never had the chance to work with them during my career, which led me to forget just how powerful and versatile they can be. For me, that moment came while working on Schemio, my interactive diagramming editor. This article dives into how I used matrices to solve some tricky problems, and it’s for everyone who’s curious about the math behind it.

Linear Algebra, Programming, Web Development, Software Engineering, Diagramming Tools

298 points by binshu 107 days ago | 46 comments

New textbook teaches students about matrix methods and their real world apps (engin.umich.edu)
A new textbook, Linear Algebra for Data Science, Machine Learning, and Signal Processing, is being unveiled for use in classes that explore the many applications of matrix methods to real world data.

Linear Algebra, Data Science, Machine Learning, Signal Processing, Education

77 points by teleforce 142 days ago | 33 comments

Transforming Colors with Matrices (lisyarus.github.io)
There's one trick we use at work, and now I'm using in my current medieval village building game project, which apparently isn't as well-known as I thought: transforming colors using matrices, interpreting colors as 3D RGB or 4D RGBA vectors. In this article I'll try to explain how it works and which operations on colors can be represented this way.

Computer Graphics, Game Development, Mathematics, Linear Algebra

92 points by ibobev 174 days ago | 12 comments

Show HN: OneSparse – Open Source Accelerated Sparse Linear Algebra for Postgres (github.com/OneSparse)
OneSparse Postgres extends the PostgreSQL object relational database with the state-of-the-art SuiteSparse:GraphBLAS high performance dense/sparse linear algebra library.

Open Source, Databases, PostgreSQL, Linear Algebra, Performance

13 points by michelpp 184 days ago | 3 comments

Neat Randomized Algorithms: RandDiag for Rapidly Diagonalizing Normal Matrices (ethanepperly.com)
Consider two complex-valued square matrices and . The first matrix is Hermitian, being equal to its conjugate transpose . The other matrix is non-Hermitian, . Let’s see how long it takes to compute their eigenvalue decompositions in MATLAB:

Algorithms, Linear Algebra, Mathematics, Software

70 points by KqAmJQ7 195 days ago | 4 comments

Linear Algebra Done Right [pdf] (axler.net)

Linear Algebra, Mathematics, Education, Textbooks

85 points by nbaksalyar 214 days ago | 39 comments

Interactive Linear Algebra Dan Margalit, Joseph Rabinoff (math.gatech.edu)

Linear Algebra, Mathematics, Education

94 points by yamal4321 214 days ago | 13 comments

Linear Algebra: What matrices are (2011) (wordpress.com)

Linear Algebra, Mathematics, Education

8 points by nbaksalyar 216 days ago | 5 comments

Poor Foundations in Geometric Algebra (terathon.com)