:PROPERTIES: :ID: eac079b7-1144-4506-b8c5-4717ccac8a7b :END: #+title: Hilbert 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 A Hilbert Space $\mathcal{H}$ is an [[id:36a2715c-a8db-4b75-b799-61ce43be2d2d][inner product space]] whose inner product defines a complete metric space.