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 \(\{^A_BR, ^AP_{Borg}\}\). Here \(^A_BR\) describes the orientation of \(\{B\}\) with respect to \(\{A\}\) and \(^AP_{Borg}\) describes the origin of \(\{B\}\) with respect to \(\{A\}\).