(linguistics) A generative grammar, especially of a natural language, developed in the Chomskyan tradition of phrase structure grammars (as opposed to dependency grammars), and involving the use of defined operations called transformations to produce new sentences from existing ones.

plural of integral transform

plural of Laplace transform

plural of Lorentz transformation

(mathematics, relativity) A transformation relating the spacetime coordinates of one frame of reference to another in special relativity.

(music) A rule that modifies a well-formed structure (in limited ways). / (grammar) A rule that takes an input and changes it in some restricted way to result in a surface structure.

(geometry, linear algebra) A geometric transformation that preserves lines and parallelism, but in general not lengths or angles; (more formally) an automorphism of an affine space: a mapping of an affine space onto itself that preserves both the dimension of any affine subspace and the ratio of the lengths of any pair of parallel line segments.

plural of linear transformation

(linear algebra) A map between vector spaces which respects addition and multiplication.

(geometry, complex analysis) A transformation of the extended complex plane that is a rational function of the form f(z) = (az + b) / (cz + d), where a, b, c, d are complex numbers such that ad − bc ≠ 0; an automorphism of the complex projective line.