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+: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" />
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+
+* 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.