# Norm Functions

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)
• $$\forall \alpha \in \mathbb{R}, f(\alpha x) = | \alpha |f(x)$$

Created: 2022-02-03

Emacs 26.1 (Org mode 9.5)