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Solved: The Linear Transformation T Is Angle Preserving If T Is 1-1, And For We Have Where If There Is A Basis X1, ... ,xn Of Rn And Numbers Such That , Prove That T Is Angle Preserving If And Only If

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The linear transformation T is angle preserving if T is 1-1, and for x,y\neq 0 we have \angle(Tx,Ty)=\angle(x,y ) where \angle(x,y)=\cos^{-1}(\frac{<x,y>}{||x||_2||y||_2}).

If there is a basis x1, ... ,xn of Rn and numbers \lambda_1,...,\lambda_n such that Tx_i=\lambda_ix_i, prove that T is angle preserving if and only if all  |\lambda_i| are equal.

Also,what are all angle preserving T: R^n \rightarrow R^n?



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