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Linear fractional transformations look like \(f(x) = \frac{ax+b}{cx+d}\) for some real constants \(a,b,c,d\). Perhaps I can convince you they are fractional, but how are they linear? Considering the simplest example, how could something like \(f(x) = 1/x\) be linear? We’d try to show that to some extent, it is linear. The main idea is that we embedd the real line into the cartesian plane and cheat a bit by using projections. Consider the transformation \(r: (x,y) \to (y,x)\). This is nothing mor...