Topic · in development — big ideas below
Linear algebra
The mathematics of many things at once.
A vector is a list of numbers treated as one object; a matrix transforms whole collections of them in a single move. Linear algebra is how mathematics handles a thousand variables with the same ease as one.
The big ideas
Vectors are arrows and lists
One object, two views: an arrow with direction and length, or a column of coordinates. Fluency means switching between them freely.
Matrices are verbs
A matrix isn't a grid of numbers to stare at — it's an action: rotate, stretch, project, shear. Multiplying applies the action.
Eigenvectors are the grain of a transformation
Most vectors get knocked off course by a transformation. A few special ones only stretch. Find them and you've found the transformation's skeleton.
Out in the world
Machine learning
Data is matrices; models are matrix operations. GPUs exist because of linear algebra.
3D graphics
Every camera move and object rotation in a game is a 4×4 matrix multiplication.
Search & recommendations
PageRank and recommender systems are eigenvector problems at web scale.
The planned course
- 01VectorsArrows, lists, addition, scaling — the atoms.soon
- 02The dot productOne number that measures alignment.soon
- 03Matrices as transformationsWatch the plane move.soon
- 04Systems of equations, revisitedMany equations, one matrix.soon
- 05Determinants & inversesWhen transformations can be undone.soon
- 06Eigenvectors & eigenvaluesThe directions a transformation can't bend.soon
While you wait — this connects to material that's live now