# Definition In an [[Inner Product Space]], an orthogonal basis $\mathcal{B} = \{\pmb{e}_i\}_{i=1\ldots n}$ is one characterized by: $ \braket{\pmb{e}_i|\pmb{e}_j} = c_{ij}\delta_{ij} $ where $c_{ii} \neq 0$. If $c_{ii} = 1 \forall i$ then the basis is called orthonormal.