Show that a Möbius transformation has 0 and oc as its only fixed points iffit is a dilation, but not the identity.Let T be a Möbius transformation with fixed points z₁ and 22. If S is also aMöbius transformation show that S-TS has fixed points the points S-¹₁and S-¹22.

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Answered: Show that a Möbius transformation has 0…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.CR: Review Exercises

Problem 21CR: Let T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find...

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Show that a Möbius transformation has 0 and oo as its only fixed points iff it is a dilation, but not the identity. Let T be a Möbius transformation with fixed points z₁ and 22. If S is also a Möbius transformation show that S-TS has fixed points the points S-¹₁ and S-¹22.