Angle preserving transformations

[bigli]

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!

 

[CompuChip]

Try looking up Hermitian operators somewhere.