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Function that applies a set to itself
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
Transformation_(function)
Geometric transformation that preserves lines but not angles nor the origin
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
Affine_transformation
Concurrency control method for collaborative software
defined as operation context-based pre- and post- transformation conditions for generic OT functions; Third, it was defined as specific operation verification
Operational_transformation
Mathematical function, in linear algebra
Boolean function Bounded operator – Kind of linear transformation Cauchy's functional equation – Functional equation Continuous linear operator – Function between
Linear_map
Mathematical transformation
involutive transformation on real-valued functions that are convex on a real variable. Specifically, if a real-valued multivariable function is convex
Legendre_transformation
Order-preserving mathematical function
monotonic transformation (or monotone transformation) may also cause confusion because it refers to a transformation by a strictly increasing function. This
Monotonic_function
Bijection of a set using properties of shapes in space
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
Geometric_transformation
Operation on formal power series
In mathematics a transformation of a sequence's generating function provides a method of converting the generating function for one sequence into a generating
Generating function transformation
Generating_function_transformation
Central object in linear algebra; mapping vectors to vectors
_{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
Transformation_matrix
Function in statistics
learning, especially in data transformations. Mathematically, the logit is the inverse of the standard logistic function σ ( x ) = 1 / ( 1 + e − x )
Logit
Topics referred to by the same term
Transformation (function), concerning functions from sets to themselves. For functions in the broader sense, see function (mathematics). Affine transformation, in
Transformation
Computer image processing technique
equalization (AHE) improves on this by transforming each pixel with a transformation function derived from a neighbourhood region. It was first developed for
Adaptive histogram equalization
Adaptive_histogram_equalization
Concept in linear algebra
algebra, a Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a reflection
Householder_transformation
Limiting form of small transformation
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
Infinitesimal_transformation
Partial differential equation
The Cole–Hopf transformation, developed independently by Julian D. Cole and Eberhard Hopf in 1950, is a change of variables that allows to transform a
Cole–Hopf_transformation
Planar movement within a Euclidean space without rotation
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
Translation_(geometry)
Application of a function to each point in a data set
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
Data transformation (statistics)
Data_transformation_(statistics)
conformal linear transformation, also called a homogeneous similarity transformation or homogeneous similitude, is a similarity transformation of a Euclidean
Conformal linear transformation
Conformal_linear_transformation
transformation semigroup (or composition semigroup) is a collection of transformations (functions from a set to itself) that is closed under function
Transformation_semigroup
Theory of cryptography
an "entropy pool", with input "poured into" the pool, and the transformation function referred to as "stirring the entropy pool". Note that input bits
Sponge_function
Isomorphism of projective spaces in geometry
where }}ad-bc\neq 0,} which are called homographic functions or linear fractional transformations. In the case of the complex projective line, which can
Homography
Geometric transformation combining reflection and translation
In geometry, a glide reflection or transflection is a geometric transformation that consists of a reflection across a hyperplane and a translation ("glide")
Glide_reflection
Transformation method within a three-dimensional space
compute transformations between datums. The Helmert transformation is also called seven-parameter transformation. The Helmert transformation can be expressed
Helmert_transformation
Statistical transformation
Fisher transformation. To derive the Fisher transformation, one starts by considering an arbitrary increasing, twice-differentiable function of r {\displaystyle
Fisher_transformation
Generalized scaling operation in geometry
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
Homothety
Geometric transformation
affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale
Scaling_(geometry)
Transformation of coordinates through an angle
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
Rotation of axes in two dimensions
Rotation_of_axes_in_two_dimensions
Transformation of a geometric space preserving structure
rendering physical motion into expression as mathematical transformation. Frequently the transformation can be written using vector algebra and linear mapping
Motion_(geometry)
Mathematical operation in quantum optics, general relativity and other areas of physics
The Bogoliubov transformation is often used to diagonalize Hamiltonians, with a corresponding transformation of the state function. Operator eigenvalues
Bogoliubov_transformation
Process that changes pixel intensity
centered. Gamma correction (log/inverse log) is also a common transformation function. Intensity operations generally operate on a colorspace that maps
Normalization (image processing)
Normalization_(image_processing)
functionalization (LSF) is a desired, chemical or biochemical, chemoselective transformation on a complex molecule to provide at least one analog in sufficient quantity
Late-stage_functionalization
Family of linear transformations
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that
Lorentz_transformation
Generalization of the Legendre transformation
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
Convex_conjugate
Transformation of coordinates that moves the origin
similarly. A translation of axes is a rigid transformation, but not a linear map. (See Affine transformation.) Coordinate systems are essential for studying
Translation_of_axes
Estimation method
transform (UT) is a mathematical function used to estimate the result of applying a given nonlinear transformation to a probability distribution that
Unscented_transform
Matrix representing a Euclidean rotation
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
Rotation_matrix
Rational function of the form (az + b)/(cz + d)
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
Möbius_transformation
Analytic function on the upper half-plane with a certain behavior under the modular group
the transformation law is not an exact symmetry of the function, but more like the transformation law of a quasiperiodic function: the function picks
Modular_form
Practice of funding long-term assets with short-term liabilities
2014). "Rollover Risk and the Maturity Transformation Function of Banks". Bank of Canada Working Paper 2014–8. Maturity Transformation, Brad DeLong v t e
Maturity_transformation
Function that returns its argument unchanged
mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the value
Identity_function
Family of functions to transform data
transform is a family of functions applied to create a monotonic transformation of data using power functions. It is a data transformation technique used to
Power_transform
Theorem of convex functions
concave transformations). Jensen's inequality generalizes the statement that the secant line of a convex function lies above the graph of the function, which
Jensen's_inequality
Mathematical relation assigning a probability event to a cost
optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one
Loss_function
Proto-oncogene derived from polyomavirus SV40
transcriptional co-activators p300 and CBP, which may contribute to its transformation function. Similar proteins from related viruses are known as large tumor
SV40_large_T_antigen
Type of function in mathematics
an analytic function is a function that is locally represented by a convergent power series. More precisely, a real or complex function is analytic at
Analytic_function
Branch of mathematics studying functions of a complex variable
holomorphic functions, which are differentiable functions of a complex variable. In contrast with a differentiable real function, a holomorphic function is always
Complex_analysis
streams) and GIWs' ecological functions in five categories: source, sink, refuge, transformation and lag functions. These functions depend on the level of connectivity
Vulnerable_waters
Mathematical function that preserves angles
conformal map to another plane domain, the transformation is also harmonic. For this reason, any function which is defined by a potential can be transformed
Conformal_map
Topics referred to by the same term
"Transform", a song by Your Memorial from Redirect, 2012 Transformation (function), concerning functions from sets to themselves Transform theory, theory of
Transform
Diagnostic plot of binary classifier ability
alarms) on non-linearly transformed x- and y-axes. The transformation function is the quantile function of the normal distribution, i.e., the inverse of the
Receiver operating characteristic
Receiver_operating_characteristic
Classification algorithm
A whitening transformation or sphering transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix
Whitening_transformation
Polynomial function of degree 3
there are only three graphs of cubic functions up to an affine transformation. The above geometric transformations can be built in the following way, when
Cubic_function
Mathematical transform that expresses a function of time as a function of frequency
takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output
Fourier_transform
Concept in network engineering
{\displaystyle f} is an arbitrary transformation function. For f {\displaystyle f} to be a valid transformation function: f ( x ) ∈ [ 0 , 1 ] {\displaystyle
Fairness_measure
Operation on mathematical functions
functions f: X → X, g: X → X having the same domain and codomain; these are often called transformations. Then one can form chains of transformations
Function_composition
Type of cipher
constituting transformation functions have the same structure is called an iterative cipher with the term "rounds" applied to the functions themselves.
Product_cipher
In the theory of special functions, Whipple's transformation for Legendre functions, named after Francis John Welsh Whipple, arise from a general expression
Whipple_formulae
Instantaneous rate of change (mathematics)
approximation to the graph of the original function. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given
Derivative
Transforming data by taking the logarithm
In statistics, the log transformation is the application of the logarithmic function to each point in a data set—that is, each data point zi is replaced
Log transformation (statistics)
Log_transformation_(statistics)
Mathematical function having a characteristic S-shaped curve or sigmoid curve
general form of a unitary sigmoid function is y=AS(f(x))+B, where S is an increasing sigmoid function, f(x) is a transformation of the independent variable
Sigmoid_function
Coordinate transformation that preserves the form of Hamilton's equations
derivative of a function known as a generator, which reduces to being only a function of time for restricted canonical transformations. In addition to
Canonical_transformation
Adoption of digital technology by an organisation
Digital transformation (DT) is the process of adoption and implementation of digital technology by an organization in order to create new or modify existing
Digital_transformation
Function defined by a hypergeometric series
hypergeometric function 2F1(a, b; c; z) is a special function represented by the hypergeometric series, that includes many other special functions as specific
Hypergeometric_function
Box–Cox transformation becomes: y = e z , {\displaystyle y=e^{z},} an exponential model. Therefore, the original inverse Box-Cox transformation contains
Response_modeling_methodology
Smooth approximation of one-hot arg max
The softmax function, also known as softargmax or normalized exponential function, converts a tuple of K real numbers into a probability distribution
Softmax_function
Association of one output to each input
mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the
Function_(mathematics)
Function related to statistics and probability theory
A likelihood function (often simply called the likelihood) gives the relative merit of various statistical models for describing a data set. Often the
Likelihood_function
Complex-differentiable (mathematical) function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood
Holomorphic_function
Mathematical function
identifying the transformation, γi is a multiplication factor common to these three functions, and the prime indicates the transformed function. The other
Jacobi_elliptic_functions
Vector-valued function of multiple vectors, linear in each argument
multilinear map is a function of several variables that is linear separately in each variable. More precisely, a multilinear map is a function f : V 1 × ⋯ ×
Multilinear_map
Family of authenticated ciphers
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
Ascon_(cipher)
Physics concept
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
Covariant_transformation
Class of statistical models
This can be avoided by using a transformation like cloglog, probit or logit (or any inverse cumulative distribution function). A primary merit of the identity
Generalized_linear_model
Generalization of definite integrals to functions of multiple variables
domain has a circular symmetry and the function has some particular characteristics one can apply the transformation to polar coordinates (see the example
Multiple_integral
flag variety that are defined in terms of a Hessenberg function h and a linear transformation X. The study of Hessenberg varieties was first motivated
Hessenberg_variety
Endomorphism preserving the inner product
spaces (such as Hilbert spaces). In other words, a unitary transformation is a bijective function U : H 1 → H 2 {\displaystyle U:H_{1}\to H_{2}} between two
Unitary_transformation
Element mapped to itself by a mathematical function
change under a given transformation. Specifically, for functions, a fixed point is an element that is mapped to itself by the function. Any set of fixed
Fixed_point_(mathematics)
Danish sociologist of law and legal theorist
constituted. In the edited volume The Law of Political Economy: Transformation in the Function of Law, the law of political economy is presented as a socio-legal
Poul_F._Kjaer
Mathematical tool
partial differential equations, and each of the two functions is then said to be a Bäcklund transformation of the other. A Bäcklund transform which relates
Bäcklund_transform
Converting data between different formats
In computing, data transformation is the process of converting data from one format or structure into another format or structure. It is a fundamental
Data transformation (computing)
Data_transformation_(computing)
Functions in mathematics
the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R {\displaystyle f\colon U\to \mathbb
Harmonic_function
Matrix of partial derivatives of a vector-valued function
The transformation from polar coordinates (r, φ) to Cartesian coordinates (x, y), is given by the function F: R+ × [0, 2π) → R2 with
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Value that appears most often in a set of data
random variable, the mode is the value x at which the probability mass function P(X) takes its maximum value, i.e., x = argmaxxi P(X = xi). In other words
Mode_(statistics)
Class of mathematical function
In complex analysis, a meromorphic function on an open subset D {\displaystyle D} of the complex plane is a function that is holomorphic on all of D {\displaystyle
Meromorphic_function
Maps whose domain and codomain are acted on by the same group, and the map commutes
and when the function commutes with the action of the group. That is, applying a symmetry transformation and then computing the function produces the
Equivariant_map
Description of continuous random distribution
probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function whose value at any given
Probability_density_function
Mapping involving integration between function spaces
integral transform is a type of transformation that maps a function from its original function space into another function space via integration, where some
Integral_transform
Integral transform useful in probability theory, physics, and engineering
of the Riemann zeta function, and his method is still used to relate the modular transformation law of the Jacobi theta function, which is readily proved
Laplace_transform
Concept in applied statistics
The aim behind the choice of a variance-stabilizing transformation is to find a simple function ƒ to apply to values x in a data set to create new values
Variance-stabilizing transformation
Variance-stabilizing_transformation
Function that is holomorphic on the whole complex plane
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane
Entire_function
Coordinate transformation of raster or vector dataset in geographic space
Georeferencing or georegistration is a type of coordinate transformation that binds a digital raster image or vector database that represents a geographic
Georeferencing
Function whose actual domain of definition may be smaller than its apparent domain
a function which is injective may be inverted to a bijective partial function. The notion of transformation can be generalized to partial functions as
Partial_function
Probability of survival beyond any specified time
certain time. The survival function is also known as the survivor function or reliability function. The term reliability function is common in engineering
Survival_function
Mathematical method in elliptic functions
Landen's transformation is a mapping of the parameters of an elliptic integral, useful for the efficient numerical evaluation of elliptic functions. It was
Landen's_transformation
Function that takes two inputs
linear transformations. A bilinear transformation, like any binary function, can be interpreted as a function from X × Y to Z, but this function in general
Binary_function
Transformation of a polynomial induced by a transformation of its roots
polynomial transformation consists of computing the polynomial whose roots are a given function of the roots of a polynomial. Polynomial transformations such
Polynomial_transformation
Distribution function associated with the empirical measure of a sample
an empirical distribution function (a.k.a. an empirical cumulative distribution function, eCDF) is the distribution function associated with the empirical
Empirical distribution function
Empirical_distribution_function
Signal representation
statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency (and possibly phase), rather than
Frequency_domain
Branch of music theory
transformations on that space. Transformations are modeled as functions acting on the entire space, meaning that every transformation must be applicable to every
Transformational_theory
Genetic alteration of a cell by uptake of genetic material from the environment
In molecular biology and genetics, transformation is the genetic alteration of a bacterial cell resulting from the direct uptake and incorporation of exogenous
Genetic_transformation
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