plural of natural transformation

plural of Lorentz transformation

plural of transformation matrix

plural of transformation matrix

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

plural of Helmert transformation

A kind of transformation in three-dimensional space, frequently used in geodesy to avoid distortion when converting from one datum to another.

(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.)

the adoption of digital technology by an organisation

(category theory) A natural transformation whose naturality squares are pullbacks.