> [!Definition] Definition (Orthonormal Set of Real Vectors) > Let $n\geq 1$ and $\mathbb{R}^{n}$ denote the [[Real n-Space|real n-space]]. A set of vectors $\underline{v}_{1},\dots,\underline{v}_{s}\in \mathbb{R}^{n}$ is *orthonormal* iff the [[Dot Product in Real n-Space|dot product]] of every pair: $\underline{v}_{i}\cdot \underline{v}_{j} = \delta_{ij}$ for each $i,j=1,,\dots,s$ where $\delta_{ij}$ is the [[Kronecker Delta Function]].