blob: 50bb154c1706d47c0ce4d090d185776c0fc612ab (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
|
:PROPERTIES:
:ID: 0ecee9ae-7786-4db0-940c-c3d64f6240f6
:END:
#+title: L_{2} space
#+author: Preston Pan
#+html_head: <link rel="stylesheet" type="text/css" href="../style.css" />
#+html_head: <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
#+html_head: <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
#+options: broken-links:t
* Introduction
The $L_{2}$ space is a [[id:9a1cc2d9-ef99-436c-8c21-9e68fd7df192][normed vector space]] with a particular norm:
\begin{align}
\label{}
(\sum_{n=0}^{N}x_{n}^{2})^{\frac{1}{2}}
\end{align}
It is easy to prove that this norm satisfies the triangle inequality, and it is even more trivial to prove
that this norm satisfies the other postulates. This norm is a part of a larger set of norms that all satisfy the
norm definition.
|
