Vector Norm

Definition

• With $V$ as a set
• Let $||\cdot ||:V\to \mathbb{R}$ be a function
• Let $|\cdot |:\mathbb{F}\to \mathbb{R}$ be an Norm Function
• The function $||\cdot ||:V\to \mathbb{R}$ is a norm if:
  1. $||r||\ge 0$ (Non-negative)
  2. $||v||=⟺v=0$ (Zero $⟺v=0$)
  3. $||\lambda v||=|\lambda |\ast ||v||$ (Distributive with scaling)
  4. $||v+w||\le ||v||+||w||$ (Triangle Inequality)