In mathematics, a transformation, transform, or self-map is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e...

generally, an affine transformation is an automorphism of an affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine...

Transformation (function), concerning functions from sets to themselves. For functions in the broader sense, see function (mathematics). Affine transformation, in...

In mathematics a transformation of a sequence's generating function provides a method of converting the generating function for one sequence into a generating...

monotonic transformation (or monotone transformation) may also cause confusion because it refers to a transformation by a strictly increasing function. This...

defined as operation context-based pre- and post- transformation conditions for generic OT functions; Third, it was defined as specific operation verification...

infinitesimal transformation that may have been recognised as such was in Euler's theorem on homogeneous functions. Here it is stated that a function F of n...

(also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V → W {\displaystyle V\to...

_{n})\end{bmatrix}}} For example, the function T ( x ) = 5 x {\displaystyle T(x)=5x} is a linear transformation. Applying the above process (suppose that...

involutive transformation on real-valued functions that are convex on a real variable. Specifically, if a real-valued multivariable function is convex...

algebra, a Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a reflection...

learning, especially in data transformations. Mathematically, the logit is the inverse of the standard logistic function σ ( x ) = 1 / ( 1 + e − x ) {\displaystyle...

such that the function is bijective so that its inverse exists. The study of geometry may be approached by the study of these transformations, such as in...

where }}ad-bc\neq 0,} which are called homographic functions or linear fractional transformations. In the case of the complex projective line, which can...

equalization (AHE) improves on this by transforming each pixel with a transformation function derived from a neighbourhood region. It was first developed for...

the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is also known as Legendre–Fenchel...

an "entropy pool", with input "poured into" the pool, and the transformation function referred to as "stirring the entropy pool". Note that input bits...

The Cole–Hopf transformation is a change of variables that allows to transform a special kind of parabolic partial differential equations (PDEs) with a...

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction...

transformation semigroup (or composition semigroup) is a collection of transformations (functions from a set to itself) that is closed under function...

The Bogoliubov transformation is often used to diagonalize Hamiltonians, with a corresponding transformation of the state function. Operator eigenvalues...

mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero...

affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale...

mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the value...

datum transformations between datums. The Helmert transformation is also called a seven-parameter transformation and is a similarity transformation. It...

} Additive inverse Coordinate rotations and reflections Householder transformation Inversive geometry Plane of rotation Reflection mapping Reflection group...

In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form f ( z ) = a z + b c z + d {\displaystyle...

In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention...

transformation is best introduced with the transformation properties of the derivative of a function. Consider a scalar function f (like the temperature at a location...

In statistics, data transformation is the application of a deterministic mathematical function to each point in a data set—that is, each data point zi...