I have read in several places, that give four points in the projective plane, with no three of them collinear, that you it is possible to create a linear change of coordinates such that the points can be written (1:0:0), (0:1:0), (0:0:1), and (1:1:1). Can someone explain to me the construction of this linear change of coordinates? Every place that I have seen this has simply stated it as fact.
2026-03-30 15:10:26.1774883426
Projective coordinate basis generated by a triangle and a fourth non-collinear point
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You should see how a plane could be created. As theory of analytical geometry states a plane can be constructed by two vectors not parallel and a given point. That means that you only need 3 non-linear points in order to make a plane.