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.

单词	similarity transformation
释义	similarity transformation 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.
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