\begin{definition}[Definition:Orthonormal Tuple of Elements of Scalar Product Space]
Let $\struct {V, \innerprod \cdot \cdot}$ be a scalar product space.
Let $v_i \in V$ for $i \in \N_{> 0}$.
Let $\tuple {v_1, \ldots, v_k}$ an ordered $k$-tuple.
Then $\tuple {v_1, \ldots v_k}$ is said to be '''orthonormal''' if:
:$\forall i,j \in \N_{> 0} : i,j \le k : \innerprod {v_i} {v_j} = \pm \delta_{ij}$
where $\delta_{ij}$ is the Kronecker delta.
\end{definition}