Volume IV · Algebra

The shared language. Vectors, maps, the arrows that only stretch.

A qubit is a vector. Attention is a matrix. Grover is a rotation. If those sentences are fog, this volume is the dictionary.

Start with a vector Skip to projection

In English

Later volumes talk about vectors, matrices, and rotations as if you already loved them. This volume is the picture: arrows, machines that move arrows, special arrows that only stretch, and dropping a perpendicular.

Try this: Start with Vector and drag. Come back whenever an LLM or qubit lab says “projection” and your eyes glaze.
Keep this: Arrows, maps, eigen, projection. That is the shared language.

The stack · click a layer

What this is

A 2D plane you can drag. Vectors, bases, 2×2 maps, composition, eigenvectors, projection — the objects hiding inside attention, gates, and Grover.

What this is not

Not a linear-algebra course and not n dimensions. The pictures are 2D so you can see them. The claims (order matters, some maps only stretch, projection is attention’s skeleton) are the real ones.