Vector Norms
Overview
A vector norm is an abstraction of the concept of the length of a vector in Euclidian space.
{% length \; of \; \vec{v} = \sqrt{v_1 ^2 + ... + v_n^2} %}
Definition
A norm is a function (denoted {% ||x|| %}) that takes a vector, and returns a non-negative real number.
- {% ||x|| \geq 0 %}
- {% ||x|| = 0 %} iff {% x=0 %}
- {% ||\lambda x || = |\lambda| || x || %}
- {% || x + y || \leq ||x|| + ||y|| %}
