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  1. For a mapping between two Euclidean spaces, is it a linear conformal mapping if and only if it is a similarity transformation?

    My answer is yes, because the Jacobian matrix of a conformal transformation is everywhere a scalar times a rotation matrix.

    Note that both allow reflection, i.e. change of orientation.

  2. Is it correct that a conformal mapping may not be an affine nor projective transformation, because it may not be linear?

Thanks and regards!

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    Could you please explain why the conformal map is a scalar times a rotation matrix? I can show it for the opposite direction but I'm stuck in the regular direction of the proof.2016-02-20

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