Automorphic collineätion criterion

Let $𝐞 0, \dots, 𝐞 𝑛$ be the standard basis of $𝕂 𝑛 + 1$ , $𝐞 𝑛 + 1 = \sum 𝑛 𝑖 = 0 𝐞 𝑖$ , and $𝐸 𝑖 = [𝐞 𝑖]$ be the corresponding points of $P G (𝑛, 𝕂)$ . Then a Collineätion $Ψ$ is an Automorphic collineätion iff $Ψ$ fixes each $𝐸 𝑖$ .¹ geo