Conformal linear transformation

A conformal linear transformation, also called a homogeneous similarity transformation or homogeneous similitude, is a similarity transformation of a Euclidean or pseudo-Euclidean vector space which fixes the origin. It can be written as the composition of an orthogonal transformation with a uniform scaling (dilation). All similarity transformations are also conformal. Similarity transformations which fix the origin also preserve scalar–vector multiplication and vector addition, making them linear transformations.

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