How to I go about proving the hyperplane reflection formula?

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

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- Dec 3rd 2011, 07:43 AMdwsmithHyperplane 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 PMjonasABRAHARe: Hyperplane Reflection formula
- Dec 3rd 2011, 03:20 PMdwsmithRe: Hyperplane Reflection formula
- Dec 3rd 2011, 03:22 PMjonasABRAHARe: Hyperplane Reflection formula
tau_v(x) = -(x'-p)=x-p, where x-p = (<v,x>/<v,v>)(v)

- Dec 3rd 2011, 03:25 PMdwsmithRe: Hyperplane Reflection formula
- Dec 3rd 2011, 03:31 PMjonasABRAHARe: 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