# similarity transformation

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## similarity transformation

[‚sim·ə′lar·əd·ē ‚tranz·fər‚mā·shən] (mathematics)

A transformation of a euclidean space obtained from such transformations as translations, rotations, and those which either shrink or expand the length of vectors.

A mapping that associates with each linear transformation

*P*on a vector space the linear transformation*R*^{-1}*PR*that results when the coordinates of the space are subjected to a nonsingular linear transformation*R*.A mapping that associates with each square matrix

*P*the matrix*Q*=*R*^{-1}*PR*, where*R*is a nonsingular matrix and*R*^{-1}is the inverse matrix of*R*; if*P*is the matrix representation of a linear transformation, then this definition is equivalent to the second definition.McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

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