Norm Functions (Norms) are functions mapping vectors to non-negative values. The norm of a vector \(x\) measures the distance from the origin to point \(x\). It must satisfy the following properties:

- \(f(x) = 0 \implies x = 0\)
- \(f(x + y) \leq f(x) + f(y)\) (the Triangle Inequality)
- \(\forall \alpha \in \mathbb{R}, f(\alpha x) = | \alpha |f(x)\)