Linear Algebra
Vectors: Arrows and Lists
7 min+60 XPStep 1/11
The arrow and the spreadsheet
A vector is two things at once, and the quiet miracle of linear algebra is that they're the same thing:
- Geometrically, it's an arrow — a direction plus a length, drawn from the origin
- Numerically, it's a list of numbers — the coordinates of that arrow's tip
The vector [3, 2] means 'walk 3 right, then 2 up.' Every list is secretly an arrow; every arrow is secretly a list.
Machine learning lives on both faces at once: your data enters as lists — hundreds of numbers per example — but everything the model does with them is geometry in disguise.
analogy
A vector is like a recipe versus the photo of the dish: two representations of one thing. The list is the recipe the computer follows; the arrow is the picture you can actually reason about.