:PROPERTIES: :ID: 3cc20d29-dc18-49cc-8fb8-27372a48e1b0 :mtime: 20231017012926 :ctime: 20231017012837 :END: #+title: orthonormal basis #+filetags: :public:project: * Definition Given a [[id:6eec1bb7-1ca7-4073-a27f-5b76917668fa][basis]] $B$, we say that $B$ is *orthonormal* if and only if for all $i,j \in \mathbb{N}$, $\vec{e}_{i} \cdot \vec{e}_{j} = \delta_{i,j}$.