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April 21st, 2012, 11:01 PM  #1 
Newbie Joined: Jan 2012 From: Tasmania, Australia Posts: 14 Thanks: 0  Finite Reflection Groups in Two Dimensions  R2
I am seeking to understand reflection groups and am reading Grove and Benson: Finite Reflection Groups On page 6 (see attachment  pages 5 6 Grove and Benson) we find the following statement: It is easy to verify (Exercise 2.1) that the vector is an eigenvector having eigenvalue 1 for T, so that the line is left pointwise fixed by T. I am struggling to see why it follows that L above is left pointwise fixed by T (whatever that means exactly!  can someone please clarify this matter?). Can someone please help  I am hoping to be able to formally and explicitly justify the statement. The preamble to the above statement is given in the attachment, including the definition of T Notes (see attachment) 1. T belongs to the group of all orthogonal transformatios, . 2. Det T = 1 For other details see attachment Peter 
April 21st, 2012, 11:03 PM  #2 
Newbie Joined: Jan 2012 From: Tasmania, Australia Posts: 14 Thanks: 0  Re: Finite Reflection Groups in Two Dimensions  R2
I forgot to upload the attachment  and so am uploading it now


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dimensions, finite, groups, reflection 
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