# Spivak correction?

1. Apr 26, 2012

### brydustin

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. Apr 26, 2012

### brydustin

.....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