DemagickedSubscribe

Learn

Start from nothing. Go all the way.

Complete subjects, taught from first principles on real data. Watch a lecture, then put your hands on it.

Volume I

Linear Algebra for Machine Learning

From a single point in space to the mathematics inside every modern model.

Start free ›Lectures 1 and 2 out now
Lecture 4b finds x
  1. A phone gallery of faces and pets, from Lecture 1

    Lecture 115:49

    Space, Distance & Similar Photos

    Your phone has never met your friend. So how does it gather forty photos of her into one pile?

    Watch ›Playground ›

  2. Vectors of two and three dimensions being added, from Lecture 2

    Lecture 222:00

    Vectors, Span & Basis

    What lives exactly halfway between a photo of a dog and a photo of a beach?

    Watch ›Playground ›

  3. A table of four patients and their risk scores, from Lecture 3

    Lecture 3Coming soon

    Matrices & Multiplication

    Four measurements go in. One risk score comes out. What happened in between?

    Playground ›

  4. Two feature arrows sweeping a flat sheet in a space of three patients’ scores, from Lecture 4a

    Lecture 4aComing soon

    Linear Equations & the Two Pictures

    We know the patients. We know the scores. What recipe sits in between?

    Playground ›

  5. The four patients, the four weights found by elimination, and their risk scores, from Lecture 4b

    Lecture 4bComing soon

    Gaussian Elimination

    How does a computer solve A x = b, in a million dimensions?

    Playground ›

Playgrounds

Every lecture has a place for your hands. Break it, and see why.

Still being made

The rest of Volume I. In the order it wants to be learned.

  1. 05

    The machine and its spaces

    Matrices as machines that move the whole of space. Span, independence and basis, made precise. The column space and the null space. Undoing the machine: inverses and LU. Rank, and the four fundamental subspaces that organise everything.

  2. Orthogonality

    Projections and least squares. Gram–Schmidt and QR. The dot product, met with a purpose. Linear regression, built from first principles.

  3. Eigenvalues

    Determinants. Eigenvalues and eigenvectors, diagonalisation, powers of a matrix. Symmetric and positive definite matrices. Change of basis.

  4. Decompositions

    The singular value decomposition. PCA, low-rank approximation, the pseudoinverse.

  5. Beyond the classical course

    Matrix calculus and backpropagation. Norms, conditioning and numerical stability. The geometry of embeddings. The linear algebra inside attention.

The complete volume.

Notes, problems, and a way to know you truly understood. Open lectures stay free.

Subscribe on YouTube@demagicked ›