normed vector space
Table of Contents
1. Introduction
A normed vector space is a vector space with a norm defined, which describes the "length" of the vector. This norm obeys these properties:
\begin{align} \label{} \lVert ax \rVert = \lvert a \rvert \lVert x \rVert \\ \lVert x + y \rVert \le \lVert x \rVert + \lVert y \rVert \end{align}this gives rise to a metric \(d(x, y)\):
\begin{align} \label{} d(x, y) = \lVert x - y \rVert \end{align}