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The determinant | Chapter 6, Essence of linear algebra

3Blue1Brown · explainer · Watch on YouTube

Pure mathematicsRecreational & visual math

What it is

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.

Why Hacker News recommends it

HN repeatedly points people to it as the clearest visual intuition for determinants, often saying it finally made the concept click.

  • 6 people recommended it
  • 6 different months
  • 4 strong recommendations
  • first 2019, last 2024

What HN commenters said

  1. “here is what a gifted presenter with the right illustrations can do in about ten minutes”

    Builds real intuition for determinants in about ten minutes with visuals.

    Chris_Newton, 2020-07 · Strong recommendation · in “How to Understand Things”

  2. “The 3Blue1Brown YouTube channel does a great job with this, introducing the determinant in terms of geometry.”

    Introduces determinants through geometry first, with excellent visualisations.

    MaxBarraclough, 2020-08 · Strong recommendation · in “Expiring vs. permanent skills”

  3. “now my mind is absolutely blown!”

    Gives intuition for determinants; the commenter's mind was blown.

    meken, 2023-02 · Strong recommendation · in “2000 Years of Matrix Multiplication”

  4. “The entire 3blue1brown series[0] on linear algebra is well worth watching, it has really intuitive graphical explanations of a bunch of concepts.”

    Intuitive graphical explanation of determinants as area and volume scaling.

    traes, 2024-11 · Strong recommendation · in “Adventures in Probability”

  5. “I didn't intuitively understand what a determinant represented or what the determinant of a transformation being zero really meant, until watching [6].”

    Gave the commenter first real understanding of what a determinant represents.

    JW_00000, 2022-10 · Recommendation · in “The paper that keeps showing up”

  6. “I have warmed up to determinants ever since I saw 3Blue1Brown give a fairly intuitive explanation for them”

    Fairly intuitive explanation of determinants that changed the commenter's view.

    3PS, 2024-04 · Recommendation · in “So what's the point of linear algebra, anyway?”

Excerpts from Hacker News comments, linked to the originals. Summaries and labels were written by a language model from those comments.

Topics: determinant, linear transformations, geometric intuition, 3blue1brown, matrices

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