The vector 2-norm

The length of a vector is most commonly measured by the “square root of the sum of the squares of the elements”. It is also known as the Euclidean norm.

Let’s try to see a specific example. Given a vector & show it on the coordinate system (x, y, z)

We can see that A point describes the coordinate of x vector. Using Pythagorean theorem, we can calculate the length of this vector

Based on this, with p >=1 the formula to get norm p is