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Math Help - Hyperplane Reflection formula

  1. #1
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    Hyperplane Reflection formula

    How to I go about proving the hyperplane reflection formula?

    \tau_v(x)=x-2<x,v>v
    Last edited by dwsmith; December 3rd 2011 at 03:21 PM.
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  2. #2
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    Cool Re: Hyperplane Reflection formula

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

    \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
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  3. #3
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    Re: Hyperplane Reflection formula

    Quote Originally Posted by jonasABRAHA View Post
    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?
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  4. #4
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    Re: Hyperplane Reflection formula

    tau_v(x) = -(x'-p)=x-p, where x-p = (<v,x>/<v,v>)(v)
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  5. #5
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    Re: Hyperplane Reflection formula

    Quote Originally Posted by jonasABRAHA View Post
    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.
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  6. #6
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    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
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