transformation

plural of transformance

The condition of being transformative

(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.

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

(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.

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

plural of linear 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).

plural of affine transformation