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Angle preserving 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 answering to this quastion is connected with eigenvalues of T.please help me!!
    Last edited: Jul 11, 2007
  2. jcsd
  3. Jul 11, 2007 #2


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    Try looking up Hermitian operators somewhere.
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