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Fredrik
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Mar2-12, 09:22 PM
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Orthogonal Transformations _ Benson and Grove on Finite Reflection Groups


Quote Quote by Math Amateur View Post
Thanks Fredrik

Definitely dealihng with case [itex] \mathbb{R^2}[/itex]

Will just reflect on what you wrote!

Still puzzling a bit about showing that [itex] T e_2 = \pm ( - \nu , \mu) [/itex]

Peter
You know that Te2 is the second column of T, that ##(\mu,\nu)## is the first column, and that the columns are orthonormal. So you only have to prove that if ##(\alpha,\beta)\cdot (\mu,\nu)=0## and ##|(\alpha,\beta)|=1##, then ##(\alpha,\beta)=\pm(-\nu,\mu)##.