Let $V$ together with $\langle\cdot,\cdot\rangle$ be a \reftext{def:complex-inner-product-space-2026a}{complex inner product space}, let $n$ be a \reftext{def:natural-numbers-2026a}{natural number}, let $[n]$ be the \reftext{def:initial-segment-natural-numbers-2026a}{initial segment} determined by $n$, and let $e:[n]\to V$ be a map with values $e_{k}$.

The family $e$ is \textbf{orthonormal} if every $e_{k}$ with $k\in[n]$ is a \reftext{def:unit-vector-2026a}{unit vector}, and $e_{j}$ and $e_{k}$ are \reftext{def:orthogonal-vectors-2026a}{orthogonal} for all $j,k\in[n]$ with $j\ne k$.