The term "similarity transformation" is used either to refer to a geometric similarity, or to a matrix transformation that results in a similarity. A similarity transformation is a conformal mapping whose transformation matrix A' can be written in the form A' congruent B A B^(-1), where A and A' are called similar matrices (Golub and Van Loan 1996, p. 311). Similarity transformations transform objects in space to similar objects. Similarity transformations and the concept of self-similarity are important foundations of fractals and iterated function systems.

affine transformation | conformal mapping | determinant | dilation | iterated function system | normal subgroup | similarity | similar matrices