linear transformations

A 10-minute 3Blue1Brown chapter explaining the determinant as the factor by which a linear transformation scales area or volume. It builds the idea geometrically with animations before any formulas.

The first chapter of 3Blue1Brown's Essence of Linear Algebra series, introducing vectors with animated geometric visuals. It begins a series that builds intuition for linear algebra from the basics.

A five-minute preview of 3Blue1Brown's Essence of Linear Algebra series, which uses animation to build geometric intuition for topics from a standard linear algebra course.

Simon Peyton Jones presents linear types for Haskell, showing how practical linearity can fit into a higher-order polymorphic language. The talk covers motivations such as resource handling and relates the ideas to Rust.

A Linear engineer talks about scaling the company's sync engine, which keeps client data local and synchronized. It follows an earlier talk on the same system.

The first lecture of Gilbert Strang's MIT 18.06 Linear Algebra course, covering the geometry of linear equations. It opens a full 35-lecture university course.

3Blue1Brown's chapter on eigenvectors and eigenvalues in the Essence of Linear Algebra series. It builds a visual intuition for what they mean, why an eigenbasis is useful, and ends with a puzzle.

Sasha Rush surveys linear RNNs and state space models as replacements for attention in transformer-style models, in a talk for MLSys. It covers the foundational preliminaries and predates Mamba.

Google engineer Dany Qumsiyeh presents a prototype automatic, non-destructive book scanner that turns pages and captures high-resolution images, built in Google's workshops. The talk includes a live demo and a short technical overview.

Huygens Optics explores the idea that space is a non-linear elastic medium, and uses simulations to show how wave energy might be confined locally into particle-like objects. It touches on inertia, the Schwinger limit and the vacuum as a medium.

Ben Vallack compares finger movement on a staggered keyboard with an ortholinear grid keyboard, using an Anne Pro 2 and a ZSA Planck EZ. He argues the stagger forces awkward finger motion.

A short test firing of the XRS-2200 linear aerospike engine at NASA Stennis Space Center, which was designed for the cancelled X-33 VentureStar. The engine is shown at roughly 80 percent of max thrust.

An 88-minute Microsoft Research talk that explains how quantum computers beat classical ones using basic linear algebra, qubits, superposition and gates. It works through the Deutsch oracle problem and ends with entanglement, teleportation and a live demo.

Patrick Boyle's deadpan account of Saudi Arabia's Neom and The Line megaproject, a planned 170 km linear city that has been scaled back to a fraction of its size. He covers the feasibility problems and the financing.

Redis Labs and Tim Davis present RedisGraph, which uses GraphBLAS to treat graph queries in Cypher as sparse linear algebra for lower latency.

The introductory lecture of Stephen Boyd's Stanford Convex Optimization I course (EE 364A). It outlines convex sets, functions and problems, and the course's coverage of least-squares, linear and semidefinite programming, duality and interior-point methods.

React Helsinki meetup recording featuring a talk on lessons with Apollo GraphQL and Linear co-founder Tuomas Artman on real-time sync for web apps. The sync talk explains Linear's local-first architecture.

Jiahao Chen's JuliaCon 2017 talk argues that vector transposes should be taken seriously in type systems and linear algebra libraries. It explains why treating vectors as matrices causes trouble in languages.

Steven Wittens' JSConf US 2013 talk on drawing with WebGL, using animated visuals to walk through vectors, matrices and the rendering pipeline. Despite the title, it works as a visual primer on the linear algebra behind 3D graphics.

A short conference talk from !!Con 2017 in which Kevin Chen explains the HDR imaging algorithm from a foundational paper, framing it as a system of linear equations, and implements it in a Microsoft Excel spreadsheet. No prior image processing knowledge is needed.

Martin Kleppmann's Strange Loop talk on database transactions, covering why they were dropped by NoSQL, their reputation for being slow, and newer algorithms that make serializable transactions perform and scale. It touches on consistency, linearizability and the CAP theorem.

Tom 7 (suckerpinch) delivers a long, comedic digression on gradient descent and floating-point imprecision. He shows how rounding behavior can supply the nonlinearity needed to build a neural network.

Tom Scott visits ThyssenKrupp's test tower in Rottweil to see the Multi, a rope-free elevator that uses linear motors to move cabins sideways as well as vertically.

The first video in a 55-part series by Michel van Biezen that introduces the Kalman filter and builds from the rationale through algebraic examples to the full matrix treatment. The videos are short, blackboard-style lectures.

The opening lecture of Steve Brunton's Control Bootcamp, covering the kinds of control and why closed-loop feedback matters. It starts a series that follows the control chapter of the Brunton and Kutz data-driven science book.

3Blue1Brown, in collaboration with minutephysics, introduces the math of superposition and quantum states using polarized light. It builds up the quantum behavior of photons as a simple counting and probability problem.

MinutePhysics explains that computers store brightness nonlinearly, so blurring and blending colors in raw RGB gives wrong, dark results. It shows why mixed colors, such as in gradients, look off.

Yaron Minsky of Jane Street shows how the OCaml Incremental library lets trading UIs express data transformations that are easy to read and efficient on streaming data. It includes a live table demo.

Leonard Susskind opens Stanford Continuing Studies' Theoretical Minimum series with an introduction to quantum mechanics, a course for people who want real physics rather than popularization. It assumes some calculus and linear algebra.

Jon Bentley walks through three implementations of Hoare's Quicksort, from a dozen-line C function to a series of systematic code transformations that make the program ever simpler and more powerful. It is a Google Tech Talk on code elegance and program derivation.

Big Clive tears down a cheap eBay digital caliper, explaining its capacitive linear encoder and measuring its quiescent current. He finds it surprisingly accurate and repeatable for its price.

Guy Kawasaki's UC Berkeley Haas talk on the top ten mistakes entrepreneurs make, covering a startup from inception to exit.

CityNerd explains why traffic congestion grows nonlinearly as more cars use a road network, and why adding road capacity tends not to fix it. It covers the consequences for drivers, bus riders, cyclists and pedestrians, and discusses alternatives such as true bus rapid transit.