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What does Möbius transformation mean?

Looking for the meaning or definition of the word Möbius transformation? Here's what it means.

Noun
  1. (geometry, complex analysis) A transformation of the complex plane that is a rational function of the form f(z) = (az + b) / (cz + d), where a, b, c, d are complex numbers such that ad - bc ≠ 0.
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