Vectors

A vector can be seen in three ways, and a good mathematician switches between them depending on what is needed.

• An arrow. It has a direction and a length. This is how a physicist sees it.
• A list of numbers. For example $(3, 2)$. This is how a programmer sees it.
• A point. The tip of an arrow that starts at the origin.

Adding and scaling

You add two vectors component by component. You multiply a vector by a number by multiplying every component.

import numpy as np

u = np.array([3, 2])
v = np.array([1, 4])

print("sum:", u + v)
print("double:", 2 * u)
print("length of u:", np.linalg.norm(u))

The length of a vector

You get the length from the Pythagorean theorem. The arrow $(3, 2)$ is the hypotenuse of a triangle with legs $3$ and $2$.