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Mathematics you can see

Vectors, determinants, eigenvectors, and Fourier analysis explained through pictures and geometric intuition.

7 videos · 2 hours 9 min

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  1. 01

    Vectors | Chapter 1, Essence of linear algebra

    3Blue1Brown · 17 HN recommendations

    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.

  2. 02

    The determinant | Chapter 6, Essence of linear algebra

    3Blue1Brown · 6 HN recommendations

    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.

  3. 03

    Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra

    3Blue1Brown · 6 HN recommendations

    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.

  4. 04

    But what is a Fourier series? From heat flow to drawing with circles | DE4

    3Blue1Brown · 4 HN recommendations

    3Blue1Brown introduces Fourier series, from the heat equation to drawing arbitrary shapes with rotating circles. It builds a visual intuition for decomposing functions into sine waves.

  5. 05

    But what is the Fourier Transform? A visual introduction.

    3Blue1Brown · 16 HN recommendations

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

  6. 06

    The Fast Fourier Transform (FFT): Most Ingenious Algorithm Ever?

    Reducible · 7 HN recommendations

    Reducible's visual walkthrough of the Fast Fourier Transform, motivated by polynomial multiplication. It shows how the FFT's key ideas can be discovered by asking the right questions.

  7. 07

    The more general uncertainty principle, regarding Fourier transforms

    3Blue1Brown · 7 HN recommendations

    3Blue1Brown shows how the uncertainty principle arises from Fourier transforms. A wave packet cannot be narrow in both position and frequency, so the principle is a property of waves rather than of measurement.