norm

The norm tells us the size of a mathematical object in a certain space.

$p^{th}$ norm:

$$\text{displaylines}\Vert x{\Vert }_p=(\sum _{i=1}^n|x{|}^p{)}^{\frac{1}{p}}$$

We take the absolute value of $x$ because uneven $p$ could yield negative values.

Animation of different $p-\text{norms}:$

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$p=1$ is also reffered to as manhattan norm because with that norm, it is like driving through city blocks (straight lines, no diagonals)

$p=2$ is also known as the euclidean norm

References

Visualizing the circles of p-norms (Medium)
https://en.wikipedia.org/wiki/Lp_space

mathematics