Definition (Reference frame)

Let $V=\mathbb{R}^{3}$ be a Vector Space. We define a reference frame as three orthogonal unit-length vectors which can be represented as a column matrix of vectors, referred to as a vectrix: $$\mathcal{F}_{a}:=\begin{bmatrix}\vec{a}_{1} \\ \vec{a}_{2} \\ \vec{a}_{3}\end{bmatrix}$$where $\vec{a}_{i}\in V,i=1,2,3$.