plural of transformation matrix

plural of transformation matrix

(linear algebra) A matrix (of dimension n×m) that represents some linear transformation from ℝᵐ→ℝⁿ.

(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 transformational grammar

(mathematics) Given a function f(x,y,z,...) which is concave up with respect to x (i.e., its second derivative with respect to x is greater than zero), an involutive procedure for replacing x with another variable, say p=∂f/∂x thus yielding another function, say F=F(p,y,z,...). This new function contains all of the information of the original f encoded, as it were, within it so that ∂F/∂p=x and applying a similar transformation to F yields the original f. The formula is: F(p,y,z,...)=p·x(p)-f(x(p),y,z,...) where x must be expressed as a function of p. (Note: The concave upwardness means that ∂f/∂x is monotonically increasing, which means that p as a function of x is invertible, so x should be expressible as a function of p.)

(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 Lorentz transformation

the adoption of digital technology by an organisation

(physics) A unitary transformation of the orthonormal basis in which both the Hamiltonian and the state are represented; it has applications in high-energy physics.