\begin{definition}[Definition:Orthogonal (Linear Algebra)/Set]
Let $\struct {V, \innerprod \cdot \cdot}$ be an inner product space.
Let $S = \set {u_1, \ldots, u_n}$ be a subset of $V$.
Then $S$ is an '''orthogonal set''' {{iff}} its elements are pairwise orthogonal:
:$\forall i \ne j: \innerprod {u_i} {u_j} = 0$
\end{definition}