🧮 Partial Differential Equations: When Change Happens in More Than One Direction

📍 The Mathematics Behind Heat, Waves, Fluids and Modern Engineering

The Geometric Tool That Solved Einstein’s Relativity Problem | Quanta Magazine

Tensors are used all over math and science to reveal hidden geometric truths. What are they?

The thing that makes 4-bit AI work is a grid of nothing but +1s and -1s called a Hadamard matrix. Here's how a 159 year old matrix ended up…

The thing that makes 4-bit AI work is a grid of nothing but +1s and -1s called a Hadamard matrix. Here's how a 159 year old matrix ended up rescuing modern AI model performance: In 1867 James Joseph Sylvester was studying how to color tiles. He found you could build square grids…

Matmul Flow | AI by Hand Academy

nvidia's B200 does 1,760 TFLOPS on a square GEMM and 4 TFLOPS on a skinny one. the shape of your matmul is the single biggest variable in…

Linear Algebra Algorithms Taxonomy: Complete Guide

Comprehensive taxonomy of linear algebra algorithms with Python & Ruby implementations. Covers vector operations, eigenvalues, SVD, decompositions, and BLAS/LAPACK routines.

Tensordyne Claims 8x AI Efficiency Boost Over NVIDIA Using Logarithmic Math

The idea isn't novel, but presents major challenges. Tensordyne thinks it has solved them, and promises massive speed and efficiency gains as a result.

By using Logarithmic Number Systems (LNS), you can slash both the energy cost and silicon area cost of AI inference computations. How much? Tensordyne says that its upcom

Because AI compute is primarily composed of matrix multiplication, this radically simplifies the workload, and allows the functional units of Tensordyne's chip to be significantly smaller. In turn, more of the die can be SRAM cache (6x as much versus the competition), which improves both…

Hilbert space: treating functions as vectors - Eli Bendersky's website

the-litte-book-of/linear-algebra: There is hardly any theory which is more elementary than linear algebra, in spite of the fact that…

There is hardly any theory which is more elementary than linear algebra, in spite of the fact that generations of professors and textbook writers have obscured its simplicity by preposterous calcul...

Derivatives, Gradients, Jacobians and Hessians – Oh My!

This article explains how these four things fit together and shows some examples of what they are used for. Derivatives Derivatives are the most fundamental concept in calculus. If you have a funct…

How to Interpret Matrix Expressions — Transformations

Matrix algebra for a data scientist

Immersive Math

Matrix Product Interpretations and Visualizations

Matrix Product Interpretations and Visualizations: Learn Linear Algebra from scratch. Build a foundation for Machine Learning and other key technologies.

Matrix Calculus

MatrixCalculus provides matrix calculus for everyone. It is an online tool that computes vector and matrix derivatives (matrix calculus).

Linear Algebra: LU Decomposition, with Python

Part 4: A comprehensive step-by-step guide to solving a linear system with LU Decomposition

What Is an Eigenvalue? – Nick Higham

An eigenvalue of a square matrix $LATEX A$ is a scalar $latex \lambda$ such that $latex Ax = \lambda x$ for some nonzero vector $latex x$. The vector $latex x$ is an eigenvector of $LATEX A$ and it…

Supply Chain Process Optimization using Linear Programming

Understand how linear programming can be the most powerful tool for a supply chain continuous improvement engineer

Linear Algebra for Data Science - KDnuggets

In this article, we discuss the importance of linear algebra in data science and machine learning.

Probabilistic Numerics | Textbooks

Quantifying Uncertainty in Computation.

Introduction to Applied Linear Algebra: Norms & Distances

This article gives an introduction to vector norms, vector distances and their application in the field of data science

Large scale eigenvalue decomposition and SVD with rARPACK | R-bloggers

In January 2016, I was honored to receive an “Honorable Mention” of the John Chambers Award 2016. This article was written for R-bloggers, whose builder, Tal Galili, kindly invited me to write an introduction to the rARPACK package. A Short Story of rARPACK Eigenvalue…

Efficient matrix multiplication

Efficient matrix multiplication · GitHub

[2106.10860v1] Multiplying Matrices Without Multiplying

Multiplying matrices is among the most fundamental and compute-intensive operations in machine learning. Consequently, there has been significant work on efficiently approximating matrix...

Poisson's Equation is the Most Powerful Tool not yet in your Toolbox

Poisson's Equation is an incredibly powerful tool...

The torch.linalg module: Accelerated Linear Algebra with Autograd in PyTorch

Linear algebra is essential to deep learning and scientific computing, and it’s always been a core part of PyTorch. PyTorch 1.9 extends PyTorch’s support for linear algebra operations with the torch.linalg module. This module, documented here, has 26 operators, including faster…

What Happens When Multipliers No Longer Define AI Accelerators?

Current custom AI hardware devices are built around super-efficient, high performance matrix multiplication. This category of accelerators includes the

numerical-linear-algebra/README.md at master · fastai/numerical-linear-alge

Free online textbook of Jupyter notebooks for fast.ai Computational Linear Algebra course - fastai/numerical-linear-algebra

Essential Linear Algebra for Data Science and Machine Learning - KDnuggets

Linear algebra is foundational in data science and machine learning. Beginners starting out along their learning journey in data science--as well as established practitioners--must develop a strong familiarity with the essential concepts in linear algebra.

What Really IS a Matrix Determinant?

The geometric intuition behind determinants could change how you think about them.

Matrix Multiplication Inches Closer to Mythic Goal

A recent paper set the fastest record for multiplying two matrices. But it also marks the end of the line for a method researchers have relied on for decades to make improvements.

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The Matrix Calculus You Need For Deep Learning

Most of us last saw calculus in school, but derivatives are a critical part of machine learning, particularly deep neural networks, which are trained by optimizing a loss function. This article is an attempt to explain all the matrix calculus you need in order to understand the…

Eigenvectors and Eigenvalues explained visually

Linear Algebra Cheat Sheet for Machine Learning

All of the Linear Algebra Operations that You Need to Use in NumPy for Machine Learning. The Python numerical computation library called NumPy provides many linear algebra functions that may be useful as a machine learning practitioner. In this tutorial, you will discover the…