An [[Orthogonal Basis]] is a [[Basis]] in which every [[Vector]] is [[Orthogonal]] to all others. Let $V$ be a [[Vector Space]] and the [[Set|set]] $\set{u_{0},u_{1},\dots}$ be a [[Basis]] of $V$. The [[Set|set]] is considered an [[Orthogonal Basis]] [[Biconditional|if and only if]]: $\huge\braket{u_{i}, u_{j}} = 0; \forall i,j; i\neq j$