Projective frame ($n+2\text{ points in }{\mathbb{P}}^n(\mathbb{F})$)

An ordered projective frame consists of $n+2$ projective points such that any $n+1$ representative vectors are linearly independent. After mapping the first $n+1$ points to the coordinate axes, the last point has every coordinate nonzero; rescaling those axes sends it to $[1:\cdots :1]$. This proves existence and uniqueness of the projective transformation carrying one ordered frame to another. In the projective plane a frame consists of four points, no three collinear.