How to prove that every bijective rational function (over the

protestommb

protestommb

Answered question

2022-06-17

How to prove that every bijective rational function (over the field of complex numbers) is a linear fractional transformation?

Answer & Explanation

trajeronls

trajeronls

Beginner2022-06-18Added 21 answers

Say f ( x ) / g ( x ) = t for a given t then consider the polynomial h ( x ) = f ( x ) t g ( x ). Over the complex numbers h will more than one root if f , g are not of degree 1. So the only bijections are the linear fractional transformations.

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