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diff --git a/mindmap/L_{2} space.org b/mindmap/L_{2} space.org new file mode 100644 index 0000000..50bb154 --- /dev/null +++ b/mindmap/L_{2} space.org @@ -0,0 +1,19 @@ +: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. |