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

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...

_{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...

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

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

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

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

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

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

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

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

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

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

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

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...

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

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...

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...

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

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

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

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...

derivative of a function known as generator, which reduces to being only a function of time for restricted canonical transformations. In addition to leaving...

Fisher transformation. To derive the Fisher transformation, one starts by considering an arbitrary increasing, twice-differentiable function of r {\displaystyle...

conformal linear transformation, also called a homogeneous similarity transformation or homogeneous similitude, is a similarity transformation of a Euclidean...

In geometry, a glide reflection or transflection is a geometric transformation that consists of a reflection across a hyperplane and a translation ("glide")...

and N. The initial state is transformed by applying a times the transformation function p ( p a {\displaystyle p^{a}} ). On encryption, each word of A...

} 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...

is defined similarly. A rotation of axes is a linear map and a rigid transformation. Coordinate systems are essential for studying the equations of curves...