[[Automorphic collineätion]]
# Automorphic collineätion criterion

Let $\mathbf{e}_{0}, \dots, \mathbf{e}_{n}$ be the standard basis of $\mathbb{K}^{n+1}$,
$\mathbf{e}_{n+1} = \sum_{i=0}^n \mathbf{e}_{i}$,
and $E_{i} = [\mathbf{e}_{i}]$ be the corresponding points of $\mathrm{PG}(n,\mathbb{K})$.
Then a [[Collineätion]] $\Psi$ is an [[Automorphic collineätion]] iff $\Psi$ fixes each $E_{i}$.[^2020] #m/thm/geo

> [!missing]- Proof
> #missing/proof

[^2020]: 2020\. [[Sources/@kissFiniteGeometries2020|Finite geometries]]

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