6 Projective Transformations
TOOD: Figure out how to write blueprints about definitions
Given two different values, \((x_1, y_1), (x_2, y_2) \in \mathbb {F}^2, (x_1, y_1) \neq (x_2, y_2)\), we get a linear isomorphism \(A\) such that \(A (x_1, y_1, 1) = (1, 0, 0)\) and \(A (x_2, y_2, 1) = (0, 1, 0)\).
Given a point \(p\) not on the line between \((x_1, y_1), (x_2, y_2)\), the projective transformation defined by those points doesn’t move it to infinity.
Proof
Direct calculation.