1. The problem statement, all variables and given/known data From Calculus on Manifolds by Spivak: 1-7 A Linear Transformation T:Rn -> Rn is Norm Preserving if |T(x)|=|x| and Inner Product Preserving if <Tx,Ty>=<x,y>. Prove that T is Norm Preserving iff T is Inner Product Preserving. 2. Relevant equations T is a Linear Transformation => For All x,y [tex]\in[/tex] Rn and scalar c 1. T(x+y)=T(x)+T(y) 2. T(cx)=cT(x) |x|=sqrt((x1)2+...+(xn)2) x is an n tuple i.e. x=(x1,...,xn) <x,y>=[tex]\sum[/tex]xiyi where i=1,...,n 3. The attempt at a solution I cannot see what to do here at all. I am definately missing something. I don't see how the definitions relate to help me here. It's probably something simple. Any direction or hint would be greatly appreaciated. Thank you.