Meaning of Möbius transformation

Mö'bius transforma"tion

Pronunciation: [key]
  1. a map of the complex plane to itself in which a point z is mapped to a point w by w = (az + b)/(cz + d), where a, b, c, and d are complex numbers and ad − bc does not equal zero. Also called
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.