Vectors: arrows & lists

A list of numbers is an arrow

A vector is simply a list of numbers, like $[3, 2]$. But here’s the trick that makes it powerful: you can also see it as an arrow starting at 0 and ending at the point $(3, 2)$ — three steps along x, two up y. Same thing, two pictures.

In machine learning, everything becomes a vector. A house is $[\text{size}, \text{rooms}, \text{age}]$. A pixel is $[\text{red}, \text{green}, \text{blue}]$. A word is a list of a few hundred numbers. Once something is a vector, all the math in this module works on it.

// In machine learning, every example becomes a vector: a list of numbers.
// A house: [size in m², bedrooms, age in years]
const house = [120, 3, 15]

// A colour: [red, green, blue], each 0–255
const tomato = [255, 99, 71]

// A (tiny) word embedding — you'll meet these in Module 8:
const cat = [0.8, -0.2, 0.45, 0.1]

console.log(house.length, "numbers describe the house")
console.log(cat.length, "numbers describe 'cat'")