1. ## Hyperplane Reflection formula

How to I go about proving the hyperplane reflection formula?

$\tau_v(x)=x-2v$

2. ## Re: Hyperplane Reflection formula

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

$\tau_v(x)=-x+2v$

Try going to class Dustin!

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

3. ## Re: Hyperplane Reflection formula

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?

4. ## Re: Hyperplane Reflection formula

tau_v(x) = -(x'-p)=x-p, where x-p = (<v,x>/<v,v>)(v)

5. ## Re: Hyperplane Reflection formula

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.

6. ## 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