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Angle preserving linear transformations

  1. Jul 11, 2007 #1
    If x,y of R^n (as a normed vector space) are non-zero, the angle between x and y, denoted
    <(x,y), is defined as arccos x.y/(|x||y|).
    The linear transformation T :R^n----->R^n
    is angle preserving if T is 1-1, and for x,y of R^n (x,y are non zero) we have
    <(Tx,Ty) = <(x,y).

    what are all angle preserving transformations T :R^N---->R^N ?

    I guess that this quastion is connected with eigenvalues of T.please help me!!
     
    Last edited: Jul 11, 2007
  2. jcsd
  3. Jul 11, 2007 #2

    matt grime

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    The question is not (really) about eigenvalues. It is about geometry. You need to visualize what angle preserving means. Start with the plane, and R^3 (since it is not possible to visualize higher dimensions really - you must do it by analogy).
     
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