linear algebra

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.

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.

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.

A SIGGRAPH 2019 course on geometric algebra. Charles Gunn gives an intro, then Steven De Keninck gives a programmer-focused course with live examples in ganja.js.

An animated introduction to geometric algebra, presented as a language that can describe most of physics. It was made with manim and covers multivectors and how they generalize familiar tools like cross products and quaternions.

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.

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 London Haskell talk on the algebra of algebraic data types, showing how sum and product types behave like arithmetic. It frames types as numbers obeying algebraic laws.

Freya Holmer's Dutch Game Day 2023 talk asking why vectors can't be multiplied, building from complex numbers to a single axiom and arriving at geometric algebra, quaternions and multivectors.

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.

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.

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

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.

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.

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.

Veritasium tells the history of how imaginary numbers arose from the quest for a general solution to the cubic equation, including the duels and secrecy among Renaissance mathematicians. It argues math had to give up the requirement that it mirror reality.

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.

3Blue1Brown introduces group theory and abstract groups, then builds toward classification of finite simple groups and the enormous Monster group with its 196,883 dimensions.

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.

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.

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.

Matt Parker talks Numberphile through the different kinds of numbers: algebraic, transcendental, computable, normal, and beyond. It shows how few numbers we can actually name or describe.

Eugenia Cheng gives the opening keynote at Lambda World 2017, presenting category theory as very abstract algebra whose abstraction gives it broad applicability. She applies it to everyday questions including privilege and prejudice.

Paul Chiusano's Strange Loop 2019 talk introduces Unison, an open-source functional language for distributed, elastic systems. It covers content-addressed code identified by hashes of the syntax tree, a codebase manager, and algebraic effects called abilities.

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.

Colin Smith introduces Structure and Interpretation of Classical Mechanics and his Clojure port, sicmutils. He shows how higher-order functions and a symbolic algebra system can represent Lagrangian mechanics.

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.

3Blue1Brown's animated visual introduction to the Fourier Transform, showing how a signal breaks into frequency components.

Part 1 of a lecture by physicist Albert Bartlett on the exponential function and its consequences for population growth, resource use and energy. It argues that steady growth rates quickly lead to enormous quantities.

The first video of 3Blue1Brown's Essence of Calculus series, which builds toward integrals, derivatives, and the fundamental theorem of calculus from a simple geometry question. It aims to make viewers feel they could have invented calculus themselves.

The first lecture in Bartosz Milewski's category theory series for programmers. It covers the motivation and philosophy behind category theory and why composition matters for handling complexity.

3Blue1Brown walks through a very hard Putnam competition problem and its elegant solution, emphasizing the visual intuition and the thought process behind solving it.