# Hyperplane Reflection formula

• Dec 3rd 2011, 07:43 AM
dwsmith
Hyperplane Reflection formula
How to I go about proving the hyperplane reflection formula?

$\displaystyle \tau_v(x)=x-2<x,v>v$
• Dec 3rd 2011, 03:17 PM
jonasABRAHA
Re: Hyperplane Reflection formula
Quote:

Originally Posted by dwsmith
How to I go about proving the hyperplane reflection formula?

$\displaystyle \tau_v(x)=-x+2<x,v>v$

Try going to class Dustin!

Also he said the error is: \tau_v(x)=x-2<x,v>v
• Dec 3rd 2011, 03:20 PM
dwsmith
Re: Hyperplane Reflection formula
Quote:

Originally Posted by jonasABRAHA
Try going to class Dustin!

Also he said the error is: \tau_v(x)=x-2<x,v>v

Even with changing that part, do you know how to do it?
• Dec 3rd 2011, 03:22 PM
jonasABRAHA
Re: Hyperplane Reflection formula
tau_v(x) = -(x'-p)=x-p, where x-p = (<v,x>/<v,v>)(v)
• Dec 3rd 2011, 03:25 PM
dwsmith
Re: Hyperplane Reflection formula
Quote:

Originally Posted by jonasABRAHA
tau_v(x) = -(x'-p)=x-p, where x-p = (<v,x>/<v,v>)(v)

What is x'? I don't get why you are setting x-p as a projection.
• Dec 3rd 2011, 03:31 PM
jonasABRAHA
Re: Hyperplane Reflection formula
p is a vector in the plan and x its projection (x-p) is its difference, tau_v(x) is its hyperplane reflection which we call x' the different between p and x' -is x'-p