1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Mobius Transformations, quick question concepts.

  1. Jan 8, 2014 #1
    So a mobius transformation is defined as [itex]\frac{az+b}{cz+d}[/itex]=f(z).
    Where ad-bc≠0.


    My question is just deriving this condition ad-bc≠0.

    I understand that the condition describes the case were the mapping leaves all points unchanged. This is described as undefined in some textbooks...(why is this, isn't it then just an identity map?)

    But not by setting z=f(z).

    I can't see why this condition would not equally be desribed by z=f(z)?

    Many Thanks for any assistance.
     
  2. jcsd
  3. Jan 8, 2014 #2

    maajdl

    User Avatar
    Gold Member

    If ad-bc=0 then f(z) = b/d which is a constant.
    Therefore, the equation y=f(z) can be inverted with respect to z only if ad-bc is not zero.
     
  4. Jan 8, 2014 #3
    But I can't see why this condition would not equally be desribed by z=f(z)?
     
  5. Jan 8, 2014 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I guess I don't see why anyone would describe that mapping where ad-bc=0 as 'leaving all points unchanged'. It doesn't. It maps everything into a constant.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted