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Spivak correction?

  1. Apr 26, 2012 #1
    Please read the italic part at the top of https://www.physicsforums.com/showthread.php?t=243852

    Is it true if we generalize to the complex case that an angle preserving transformation's eigenvalues are all the same magnitude? Is there a simple proof for the real case? Obviously its not a sufficient condition, but it is a necessary condition (see the link). But what's the proof.

    This is how far I can get:
    If its angle preserving, then for x,y eigenvectors (λ_x, λ_y eigenvalues) we get

    (λ_x)(λ_y)°/|λ_x||λ_y| = (λ_x)°(λ_y)/|λ_x||λ_y| = 1 where ° denotes the complex conjugate.
    But I'm not sure where to go from here..... is there a simple contradiction that can show itself?
     
  2. jcsd
  3. Apr 26, 2012 #2
    .....okay, no need for an explanation. I found a proof.
    http://christianmarks.wordpress.com/2009/07/06/spivaks-botched-problem/ [Broken]
     
    Last edited by a moderator: May 5, 2017
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