Experiments / live

A matrix is a verb playground

A matrix isn't a grid of numbers — it's a verb that grabs the plane and bends it. Drag the four sliders below to change the entries a, b, c, d of the matrix [[a, b], [c, d]] and watch the unit grid warp in real time: the two heavy arrows are where the basis vectors e₁ and e₂ land — the columns of the matrix — and the determinant reading is the signed area the unit square gets stretched into. The full story — why the columns are all a matrix needs to tell you, and what the determinant really measures — is in the essay.