Extending my [earlier question about linear transformations](https://mathoverflow.net/questions/33303/linear-transformation-takes-a-polygon-to-another-one), what's the easiest way to test if there exists a projective linear transformation that takes one polygon to another (in $\mathbb{R}\mathbb{P}^2$)?



Projective transformation between polygons.
The answer Tim Gowers and Will Jagy gave you in response to your earlier question can be extended straightforwardly. A homogeneous linear transformation on R^3 has 3x3 - 1 = 4x2 degrees of freedom, so there is a unique projective-linear transformation between any given pair of non-degenerate quadrilaterals. Thus do with quadrilaterals what was done in the previous question with triangles.


