Coordinate Frame

A coordinate frame is a set of four vectors that describes the [Orientation] and [Position] of one coordinate system with respect to another. For example, if we have a coordinate frame $\{B\}$ in $\{A\}$, then we can describe $\{B\}$ as ${\{}_B^{A}R{,}^A{P}_{Borg}\}$. Here ${}_B^{A}R$ describes the orientation of $\{B\}$ with respect to $\{A\}$ and ${}^A{P}_{Borg}$ describes the origin of $\{B\}$ with respect to $\{A\}$.