Matrices Are Verbs

Stare at a matrix like [[0, -1], [1, 0]] and it looks like a tiny spreadsheet. That's the wrong mental model.

A matrix is a function on space itself: feed in a vector, get out a moved vector. This particular one rotates the plane 90° — every arrow swings a quarter-turn counterclockwise. Other matrices stretch, shear, squash, or mirror the plane.

Once you see matrices as verbs — things that act — linear algebra stops being symbol-pushing and becomes animation.