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!!