Angle preserving transformations

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Angle preserving transformations in the context of normed vector spaces R^n are defined by the property that for any non-zero vectors x and y, the angle between their images under transformation T, denoted as <(Tx, Ty), equals the angle between x and y, <(x, y). This implies that T must be a one-to-one linear transformation. The discussion suggests a connection between these transformations and the eigenvalues of T, particularly in relation to Hermitian operators.

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bigli
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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!
 
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Try looking up Hermitian operators somewhere.
 

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