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:ID:       0ecee9ae-7786-4db0-940c-c3d64f6240f6
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#+title: L_{2} space
#+author: Preston Pan
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* 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.