(mathematics) A transform that converts a discrete time-domain signal into a complex frequency-domain representation.

plural of affine transformation

(category theory) A morphism between a pair of parallel functors such that if each object of the shared domain category subtends a correlated arrow — called a component — in the shared codomain (which arrow represents the difference between applying the second functor and the first functor to the correlated object) then each arrow of the shared domain subtends a commuting square — called a naturality square — between two components (correlated to the domain and codomain of the arrow).

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

(mathematical analysis, harmonic analysis, physics, electrical engineering) A particular integral transform that when applied to a function of time (such as a signal), converts the function to one that plots the original function's frequency composition; the resultant function of such a conversion.

(mathematics) an integral transform of positive real function f(t) to a complex function F(s); given by:

(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.

(geology) A geological fault separating two tectonic plates which are sliding horizontally in directions parallel with the fault line.

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